Wikiversity:Colloquium

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== Add an edit count requirement for autoconfirmed? ==

Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC)
: [[Wikiversity:Autoconfirmed users]]
: Are you suggesting an additional requirement? i.e., 4 days + 10 edits?
: How is it adjusted? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:57, 5 September 2026 (UTC)
:: Yes. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC)
:: @[[User:Jtneill|Jtneill]]: I said yes to your first question. As for the adjustment question, in the InitialiseSettings.php file on noc.wikimedia.org, on &lt;code&gt;wgAutoConfirmCount&lt;/code&gt; is where English Wikiversity would be added as &lt;code&gt;'enwikiversity' =&gt; 10,&lt;/code&gt;. Does my reply make sense? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 18:31, 15 September 2026 (UTC)
:As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC)
:I agree that adding an edit count requirement is a reasonable expectation before the user can become autoconfirmed. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 18:56, 6 September 2026 (UTC)
:+ 1 —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:40, 6 September 2026 (UTC)
:'''Weak support''' Generally reasonable, but I would caution that we should really make this clear for those instances where professors have students edit here and make it frictionless for them to get autoconfirmed status. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 19:42, 6 September 2026 (UTC)
: {{oppose|No support}} because I cannot see the [[Special:AbuseFilter/16|abuse filter]] cited as the primary reason and I do not know what LTAs is. I guess you don’t want support from ''ordinary'' users. ‑‑[[User:Kai Burghardt|Kays]] ([[User talk:Kai Burghardt|discuss]] • [[Special:Contributions/Kai Burghardt|contribs]]) 18:18, 14 September 2026 (UTC)
::Also some readers may be interested in this:
::* [[Wikipedia/Types of user accounts]]
::[[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 19:05, 14 September 2026 (UTC)
::: An LTA means a long-term abuser, and it means someone who is usually abusive. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 20:42, 14 September 2026 (UTC)

== Bartending Course on Wikiversity ==

I recently finished the course on [[Bartending]], and while I have experience editing on Wikipedia, this is my first Wikiversity project. If any of you have the time or interest, I could use an experienced eye to see if there's anything obviously missing from the course in terms of Wikiversity administration. I'm not sure what's active, if the course should belong in an existing school, or if there's any obvious discoverability tool I haven't implemented. Any tips are welcomed, or just a thumbs up saying it looks fine would be great. [[User:Jtneill|Jtneill]] recommended I post this here in case someone wanted to include the new course under News on the [[Wikiversity:Main Page|Main Page]]. Thanks! [[User:Sabbier|Sabbier]] ([[User talk:Sabbier|discuss]] • [[Special:Contributions/Sabbier|contribs]]) 01:24, 1 September 2026 (UTC)

:Wow! Fantastic work- I'm so impressed! Your work gives me inspiration on how to better organize the courses I'm working on. :) [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:32, 3 September 2026 (UTC)
: Awesome work. I've added this course to the [[Main Page/News|main page news]].
: We could also consider for [[Wikiversity:Featured]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:43, 5 September 2026 (UTC)
::The course [[Creating Wikiversity Courses]] is intended to provide guidance to new Wikiversity editors. I hope it is helpful and I welcome improvement suggestions. Thanks.  [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 14:08, 6 September 2026 (UTC)

== Writing news here ==

I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC)
: Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:46, 5 September 2026 (UTC)
::I wonder if you mean &lt;u&gt;Wikiversity:Main Page/News ?&lt;/u&gt;
::If so I have just checked this page and I see it only contains news for 2026 and part of 2025, even though the history indicates it was created in the 2000-decade. If you go back and check all revisions there is a wealth of (historical?) information. [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 16:28, 13 September 2026 (UTC)
::: I didn't mean that page, but yes, its history could be reconstructed into a more accessible format. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 21:37, 13 September 2026 (UTC)

== [[Wikiversity talk:Interface administrators#My thoughts about this user group]] ==

As I suggested, I would like to propose allowing permanent interface administrators on English Wikiversity. My temporary interface admin rights are about to expire soon, and I will soon create a new CfIA page (and its header). We should also have a minimum of two interface administrators. Thoughts? [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 16:44, 6 September 2026 (UTC)

:I am also in favor of this and we did discuss it pretty recently and came to a consensus on extending IA rights and lowering the administrative overhead, but not allowing indefinite at this juncture. From my perspective, since we discussed this so recently and nothing seems to have changed much, I personally would recommend holding off for a couple of years or until/unless there is some critical new information. Again, I would continue to support indef IA rights were it to come up again and think that at least two is also a sensible proposal. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:32, 6 September 2026 (UTC)
::Responding to myself so that I don't derail: I would be interested/willing to be an indef IA. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:36, 6 September 2026 (UTC)
: I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 18:24, 6 September 2026 (UTC)
:: CC to @[[User:Koavf|Koavf]]. I made a request since my IA rights are about to expire. We should also hold a separate vote to allow permanent IAs here (for this policy). [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 16:55, 7 September 2026 (UTC)

=== Votes ===
* For the record, I am creating a separate subsection for voting, whether or not we should allow permanent interface administrators. {{support}} accordingly. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 18:32, 15 September 2026 (UTC)
* {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:51, 18 September 2026 (UTC)

== Paid part-time Administrative Officer position with WikiJournal ==

[[WikiJournal User Group|WikiJournal]] is an open-access, nonprofit scholarly publisher hosted on Wikiversity. It uses the wiki format to allow authors to write and develop scholarly articles directly online. Submitted articles then undergo formal academic peer review and, when accepted, are published as citable journal articles while remaining freely accessible.

WikiJournal is seeking expressions of interest in a new part-time '''Administrative Officer''' position. The officer would support the project's day-to-day organizational work, including:

* Setting up and administering a system for tracking contractor hours and issuing payments.
* Coordinating the contracting, onboarding, timekeeping and payment of technical editors and other contractors.
* Maintaining financial, contractor and administrative records.
* Assisting with grant administration, budget tracking and reporting.
* Following up on board action items, deadlines and recurring obligations.
* Supporting recruitment and other operational tasks as needed.

This is a remote, flexibly scheduled contractor role averaging approximately '''6 hours per week'''. Compensation is proposed at '''US$25 per hour''', with up to approximately '''320 hours (US$8,000) available over the year'''.

Applicants may be based internationally, although appointment will depend on WikiJournal being able to establish a practical and legally appropriate contracting and payment arrangement in the applicant's country of residence.

Relevant experience may include administrative organization, bookkeeping or financial administration, contractor or personnel coordination, nonprofit or grant administration, Wikimedia participation, academic publishing, and open-access work. Applicants are not expected to have experience in every area.

For the complete role description and further details, see [[WikiJournal User Group/Administrative officer]].

Those interested should reply in the '''[[Talk:WikiJournal User Group#Call for interest: Administrative Officer|Call for interest: Administrative Officer]]''' discussion by '''30 September 2026''', briefly describing their relevant experience, any connection to WikiJournal or related communities, and their general availability. Expressions of interest received later may still be considered if the position has not been filled. Recommendations of potentially suitable candidates are also welcome. 
[[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 20:00, 10 September 2026 (UTC)

== Server switch - Your wiki will be read-only for a short time soon ==
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[[m:user:Trizek (WMF)|Trizek (WMF)]] 12:58, 15 September 2026 (UTC)
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      <text bytes="1683" sha1="eam9wrht5bcn4gxhgnjm331xpud2eez" xml:space="preserve">===Texts===
This course will use the [[wikibooks:Introduction_to_Psychology/Abnormal_Psychology|Abnormal Psychology]] Wikibook,  as well as online sources.

===Course Objectives===

* Students will have a better grasp of various mental disorders
* Students will be able to differentiate between mental disorders

===Course Outline===

* Introduction - When does a symptom rise to a level of disorder? And are psychiatric disorders truly abnormal if a significant percentage of the population has them?
**Assignment - Buy a cheap notebook to keep a journal for this class all in one place. Begin by reflecting on the above questions, and your expectations for the course.

&quot;Unit One - Serious and Persistent Mental Illness&quot;

*First Class Meeting - Depression
**Lecture
**Readings
***[[w:Clinical depression|Clinical Depression on Wikipedia]]

*Second Class Meeting - Bipolar Disorder
** Lecture
**Readings
***[[w:Bipolar disorder|Bipolar Disorder on Wikipedia]]
*Third Class Meeting - Schizophrenia
**Lecture
**Readings
***[[w:Schizophrenia|Schizophrenia on Wikipedia]]
*Fourth Class Meeting - Schizoaffective Disorder
**Lecture
***[[w:Schizoaffective disorder|Schizoaffective Disorder on Wikipedia]]

*Fifth Class Meeting - Community and Hospital Treatment for People with Serious and Persistent Mental Illness.
**Lecture
**Readings
***[[w:Psychiatric hospital|The Psychiatric Hospital on Wikipedia]]
***[[w:Partial hospitalization|Day Treatment or Partial Hospitalization on Wikipedia]]
***[[w:Clubhouse Model of Psychosocial Rehabilitation|Clubhouse Model for Psychosocial Rehabilitation]]

{{sfoot|Psychology}}

[[Category:Abnormal psychology]]
[[Category:Social Science courses]]</text>
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      <text bytes="2140" sha1="lge3k8maaybtfx6qzn0x0ryhczjt6x0" xml:space="preserve">Science journalism conveys reporting about science to the public. The field typically involves interactions between scientists, journalists, and the public.&lt;ref&gt;[[Wikipedia: Science journalism]]&lt;/ref&gt;

== Readings ==
* [[Wikipedia: Science journalism]]

== Activities ==
# Science Journalism [[/Activities/]]
# [[Biographical science journalism]] - analysis of science-related news articles that have a major focus on biographical information about scientists
# [[Wikipedia:Somatic cell nuclear transfer]]
# [http://www.chicagotribune.com/news/nationworld/chi-0612070028dec07,1,7299720.story?coll=chi-newsnationworld-hed Australia approves cloning for research] by Rod McGuirk, Canberra’s Associated Press bureau chief
# [[RNA World]] - [http://biology.plosjournals.org/perlserv/?request=get-document&amp;doi=10.1371/journal.pbio.0040448 RNA Silencing Sheds Light on the RNA World] by Rachel Jones
# Create and maintain recent science news content that will be displayed at the [[Portal:Science|Science Portal]].
# Help develop articles at [[n:Category:Science_and_technology|Wikinews]].
# [http://education.wikia.com/wiki/Wikiversity:_Biomedical_Research_Project Biomedical Research Project]; [http://education.wikia.com/wiki/Flu_pandemic:_The_greatest_enemy_of_all--Infectious_Disease Avian flu]
# Develop Wikimedia content related to Nobel Prizes in science.
#* [[Nobel Prize in Physiology or Medicine]]
#* [[Nobel Prize in Chemistry]]
# Make audio files that can be used both at Wikiversity and on [http://www.bitshuffle.org/wikicast/Su%27nosi WikiCast]. See: [[Biophilia Project]].

== See Also ==
* Links to the [[Science_journalism_organisations|national associations]] around the word.

==Discussion questions, essay ideas, and learning related AI prompt ideas==
* How can biased be reduced in science journalism?
* What skills and knowledge are useful in identifying bias in science journalism? 
* Is it important to be able to critically analyze supposed scientific findings and scientific paper when engaging in science journalism? If yes, why and how can it be done? 

== References ==
{{Reflist}}

[[Category:Science journalism]]</text>
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      <text bytes="2137" sha1="c08cb50xsjkms2kzhv14sihs8dnflgp" xml:space="preserve">Science journalism conveys reporting about science to the public. The field typically involves interactions between scientists, journalists, and the public.&lt;ref&gt;[[Wikipedia: Science journalism]]&lt;/ref&gt;

== Readings ==
* [[Wikipedia: Science journalism]]

== Activities ==
# Science Journalism [[/Activities/]]
# [[Biographical science journalism]] - analysis of science-related news articles that have a major focus on biographical information about scientists
# [[Wikipedia:Somatic cell nuclear transfer]]
# [http://www.chicagotribune.com/news/nationworld/chi-0612070028dec07,1,7299720.story?coll=chi-newsnationworld-hed Australia approves cloning for research] by Rod McGuirk, Canberra’s Associated Press bureau chief
# [[RNA World]] - [http://biology.plosjournals.org/perlserv/?request=get-document&amp;doi=10.1371/journal.pbio.0040448 RNA Silencing Sheds Light on the RNA World] by Rachel Jones
# Create and maintain recent science news content that will be displayed at the [[Portal:Science|Science Portal]].
# Help develop articles at [[n:Category:Science_and_technology|Wikinews]].
# [http://education.wikia.com/wiki/Wikiversity:_Biomedical_Research_Project Biomedical Research Project]; [http://education.wikia.com/wiki/Flu_pandemic:_The_greatest_enemy_of_all--Infectious_Disease Avian flu]
# Develop Wikimedia content related to Nobel Prizes in science.
#* [[Nobel Prize in Physiology or Medicine]]
#* [[Nobel Prize in Chemistry]]
# Make audio files that can be used both at Wikiversity and on [http://www.bitshuffle.org/wikicast/Su%27nosi WikiCast]. See: [[Biophilia Project]].

== See Also ==
* Links to the [[Science_journalism_organisations|national associations]] around the word.

==Discussion questions, essay ideas, and learning related AI prompt ideas==
* How can bias be reduced in science journalism?
* What skills and knowledge are useful in identifying bias in science journalism? 
* Is it important to be able to critically analyze supposed scientific findings and scientific paper when engaging in science journalism? If yes, why and how can it be done?

== References ==
{{Reflist}}

[[Category:Science journalism]]</text>
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      <contributor>
        <username>Michael Ten</username>
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      <comment>/* Discussion questions */ How can drones help to stop forest fires as needed?</comment>
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This project will attempt to assess whether or not the state of the art is currently conducive to this sort of technology, and if it is, how best to implement the technology.
__NOTOC__
Possible uses for this technology include: wireless mesh network clouds, speaker systems, lighting systems, video monitoring systems, cleaning and sanitation, shipping, reconnaissance aerial photography systems, and so forth.

Drones and unmanned arial systems are a [[Futurism|future oriented]] technology. 

* Can systems be made that can remain airborne a long period of time?
** Are solar cells currently advanced enough to allow this?
** Do other technologies exist that could allow this?
** Can this be done inexpensively?
* Can software be developed to allow:
** Communication between these devices
** The devices to remain autonomous and safe
** Communication between the ground
** The devices to remain autonomous for long periods
* Can this be done to look attractive and aesthetically pleasing?
** Can a twin blade design keep a vehicle aloft in an enclosure or in some hidden manner or other configuration?

==Workspace==
[[Image:MicroAirVehicle.jpg|200px|thumb]]
* [[/Readings/]]
* [[/Specifications/]]

== Learning Task ==
* '''(Drone)''' Explore definition of Drone and unmanned aerial vehicles.
* '''(Remote Control/Autonomous Vehicle)''' Assume is unmanned aerial vehicle is controlled by a remote control or it is designed as autonomous vehicle with optical pattern recognition. Compare those two approaches and explain the challenges, requirements and constraints!

==Discussion questions==
* Can drones potentially be used to stop gun violence? 
::[https://twitter.com/zoltan_istvan/status/915238719849762817 This idea] has been put forth to design drones that can detect gun fire and if necessary then stop the shooter within 30 seconds, instead of potentially 10-15 minutes not using drones. 
* How can [[Drone|drones]] be used in art exhibits and exhibitions? 
* How might drones be utilized for 100 years? 500 years? 10 years? 15 years?
* How can drones help to stop forest fires as needed?

==See also==
* [[Automation]]
* [[Drone]]
* [[Robotics]]

==External links==
&lt;!--the short list--&gt;
* [http://diydrones.com/ DIY Drones]
* [http://sourceforge.net/projects/zsim zSim flight simulator]
* September 2008 ''[http://technology.newscientist.com/article/dn14718-robot-spyplanes-get-new-role-as-medical-couriers.html Robot spyplanes get new role as medical couriers]''
* August 2008 ''[http://www.physorg.com/news138798224.html QinetiQ says it has broken unmanned flight record]''
* [http://www.instructables.com/id/Making-an-autonomous-boat-with-a-Raspberry-Pi-a-/ Making an Autonomous Boat Using a Raspberry Pi] - Can an aerial drone be made with and controlled by a Raspberry Pi too? 
* [https://www.youtube.com/watch?v=U7nJBFjKqAY Using Drones to Plant 20,000,000 Trees]

:&lt;small&gt;''See [[/External links/]] for the long list''&lt;/small&gt;
[[Category:Artificial intelligence]]
[[Category:Electrical engineering]]
[[Category:Projects]]
[[Category:Autonomous aerial systems]]
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  <page>
    <title>Speedcubing</title>
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      <comment>I added new topics like new methods, more algorithms sets, and hardware options for speedcubing.</comment>
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Speedcubing is the hobby of solving rubik's cubes in the shortest time possible, by the end of this topic you should be able to solve a rubik's cube and with enough practice be able to solve in under 1 minute.

[[Image:Rubiks_cube_solved.jpg|thumb|right|120px|Rubik's Cube in solved state]]


==What you need before you start==
*Rubik's cube

*Stackmat or other timing device(optional)
*Silicone based lubricant(optional)

==Syllabus==
===Beginners===
*[[/Introduction/|Lesson 1]]: Introduction to speedcubing and terminology
*[[/Cross/|Lesson 2]]: The cross and first layer
*[[/Middle/|Lesson 3]]: The middle layer

*[[/Review/|Lesson 4]]: Mid term review

*[[/Edges/|Lesson 5]]: Top cross(orienting edges)
*[[/Orienting corners/|Lesson 6]]: Orienting Corners
*[[/Permuting corners/|Lesson 7]]: Permuting Corners
*[[/Permuting edges/|Lesson 8]]: Permuting edges

===Intermediate===
*[[Topic:Speedcubing/Intermediate Lesson 1|Lesson 1a]]: Speedcubing Hardware
*Lesson 1b: How to Set Up a Speedcube
*[[Topic:Speedcubing/Intermediate Lesson 2|Lesson 2]]: F2L
*[[Topic:Speedcubing/Intermediate Lesson 3|Lesson 3]]: OLL
*[[Topic:Speedcubing/Intermediate Lesson 4|Lesson 4]]: PLL

===Advanced===
*[[Topic:Speedcubing/Advanced Lesson 1|Lesson 1]]: Finger tricks
*Lesson 2: Beyond CFOP/Intermediate
*Lesson 3: Speedcubing Terms and Vocabulary

'''&lt;big&gt;[[Topic:Speedcubing/Teachers-Students|Teachers-Students]]&lt;/big&gt;'''

|}

[[Category:Hobbies]]

{{BookCat}}</text>
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  <page>
    <title>Islam/Sunni Islam</title>
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      <comment>Background Research</comment>
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      <text bytes="3804" sha1="p6id8826ykc5690qp9ui4dz1kb26rw7" xml:space="preserve">[[File:Jiangwan Mosque - Eid Al-Adha.JPG|thumb|Sunni Muslims]]

The '''Sunni''', the largest group in Islam, and the largest religious denomination in the world.&lt;ref&gt;Religious Diversity and Children's Literature: Strategies and Resources, ‎Sandra Brenneman Oldendorf - 2011, p 156&lt;/ref&gt;. In Arabic, as-Sunnah literally means &quot;principle&quot; or &quot;path.&quot; '''The [[Sunnah]], or the behavior of Muhammad''' is described as a '''main pillar of Sunni doctrine'''. They believe...

*The first four caliphs (leaders) of the Muslim community were the rightful successors to Muhammad.  
*That God has not specified the leaders of the Muslim community after Muhammad, and that the leader has to be elected.

*Sunnis recognize four major legal traditions, or ''madhhabs'': [[Maliki]], [[Shafi'i]], [[Hanafi]], and [[Hanbali]]. All four accept the validity of the others and a Muslim might choose any one that he/she finds agreeable to his/her mind or personality.
=== Difference ===
Sunni and Shi'a Muslims differ on the legitimacy of the reigns of the Khulfa-e-Rashideen, the first four Caliphs. The Sunnis follow the Caliphates of all four, while the Shi'ites recognize only the Caliphate of Ali. This schism occurred following the death of 'Umar.

According to Sunni beliefs, Muhammad gave no specific directions as to the choosing of his successor when he died. At this time there were two customary means of selecting a leader: some had hereditary leaders such as Sultans or Kings, whilst some were appointed by the Ulema. There is no proof in the scriptures of the need of a Caliphate in Islam, however Al-Qaeda aims to establish a worldwide Caliphate through their Jihadism.

While Sunni and Shia Islam differ sharply on the conduct of a caliph and the right relations between a leader and a community, they do not differ on the underlying theory of stewardship.

In the initial stages the latter way of choosing leadership prevailed among the leading companions of Muhammad. Abu Bakr was elected as the first caliph or successor to Muhammad, with the other companions of Muhammad giving an oath of allegiance to him. The Persian citizens thought that Ali, Muhammad's cousin and son-in-law, should have succeeded him. However the appointment of the next two caliphs varied from the election of Abu Bakr. On his deathbed, Abu Bakr appointed Umar as his successor without an election by the community of scholars. Umar also altered the way his successor would be found. Before he was assassinated, Umar decided that his successor would come from a group of six. This group included Ali and Uthman, another companion of Muhammad. These six would have to establish from among themselves Umar's successor. Ultimately Uthman was chosen as Umar's successor, becoming the third Caliph. After the assassination of Uthman by the troublesome Persians, Ali was elected as the fourth Caliph.

== Background Research ==
* Sunni Muslims generally believe in:
** '''One God (Allah)''' — absolute monotheism.
** '''The Qur’an''' as the revealed word of Allah.
** '''Prophet Muhammad ﷺ''' as the final prophet and messenger.
** '''The Sunnah''' — the teachings, practices, and traditions of Prophet Muhammad ﷺ.
** '''The Five Pillars of Islam''' — Shahada, Salah, Zakat, Sawm (fasting in Ramadan), and Hajj.
** '''The six articles of faith''' — belief in Allah, His angels, His books, His messengers, the Day of Judgment, and divine decree (Qadar).
** '''The Companions (Sahabah)''' as important transmitters of the Prophet’s teachings.
** '''The four major Sunni schools of jurisprudence''': Hanafi, Maliki, Shafi‘i, and Hanbali.  Sunni Islam includes diverse theological and legal traditions, so beliefs and practices can vary among Sunni communities.

==Footnotes==
&lt;references/&gt;

[[Category:Islamic Studies]]</text>
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  <page>
    <title>Stress (psychological)</title>
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      <comment>speacing.</comment>
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      <text bytes="6592" sha1="0g4uc829jp3o23cpi4acd7nujh5tc7h" xml:space="preserve">{{medical disclaimer}}
Day-to-day life is full of stress; both on the personal and the professional fronts. [[Pressure]] of time often results in people reporting to their workplace with [https://en.wikipedia.org/wiki/Migraine migraine] attacks, body aches, mental strains, etc. Therefore, stress is a costly business affair that affects two aspects; the first is employee's health that directly affects the second which is the organization's profits. These affects happen because if the health does not allow the body to function normally, it will lead to increased [https://en.wikipedia.org/wiki/Absenteeism absenteeism], late comings and short leaves in the organization. Furthermore, this directly affect the organization's growth and profit since employees are the main source of profit generation for an organization.

Many people are beginning to focus on changing unhealthy [https://en.wikipedia.org/wiki/Habit habits] in order to achieve better lives. Diets are being modified and time is being made for [[exercise]], but countless individuals are forgetting one key aspect of their life: their [[mental health]]. Americans are being overburdened with excessive workloads {{citation needed}}. The overwhelming amount people have on their plates coupled with the pressure to succeed causes an unhealthy amount of stress in the general population. While many see their stress as normal, a lot of the population's stress may be of an unhealthy nature that can lead to great physical and mental difficulties down the road. America must become familiar with this threat and take measures to reduce it before we ‘work ourselves to death’.

== What is Stress? ==
The first definition for stress was created in 1936 by Hans Selye.  He stated that stress is ”the non-specific response of the body to any demand for change (Institute of Stress).&quot; Selye’s definition allows others to understand that stress is not merely a reaction to something bad, but a reaction to a change in situation. This definition lacks an explanation to what kind of response the body has. Stress is not only a change in a body response but more specifically a &quot;physical, mental, or emotional strain or tension (Institute of Stress).&quot;  In order for stress to form, whether it is from a good or bad situation, there must be a stressor causing tension to appear.

== What are some signs I am too stressed out? ==
Stress has long been considered a bad thing by most people. This is perhaps due to the undesirable side-effects that occur when in a stressful situation.  Stress can be a motivating factor until it reaches a particular threshold. Increased stress has been shown to increase productivity up to a certain point (Institute of Stress). Past this point, stress decreases productivity drastically, by triggering exhaustion and even sickness (Institute of Stress). Since many people’s stress has surpassed this threshold, nearly 1 million workers are absent each day. This number tripled from 1996 to 2000 (Institute of Stress).

In order for people to better understand whether or not they have too much stress in their lives, they must be able to identify the signs and symptoms of unhealthy stress levels. Some symptoms of stress include (Institute of Stress): 
{{col list|2|
* reoccurring headaches
* stuttering
* grinding teeth
* tremors/shaking
* frequent sweating
* insomnia
* nightmares
* muscle pains
* depression
* digestive difficulties
* panic attacks
* excess anxiety
* decreased appetite
* chest pains
* reduced work efficiency 
}}

== What are the physical effects of stress? ==
Unhealthy amounts of stress can have detrimental long term effects on the human body. Stress initiates a release of cortisol, norepinephrine, and serotonin (Stress and Cardiovascular disease &amp; Stress on the Brain).  Normal stress levels allow the body to recuperate following a stressful situation and to re-balance hormone levels.  On the other hand, chronic stress causes an imbalance of these hormones with excess in some areas of the body and deficiencies in others (Stress and Cardiovascular disease).   For example, chronic stress causes a surplus of cortisol in the brain.  This can lead to damage of neurons and loss of short term memory.  In addition, the sympathetic activity, which stress instigates, leads to a suppression of the immune system which may worsen allergies and lead to greater susceptibility to illnesses (Stress and Cardiovascular disease).

Another major concern chronic stress creates within the medical community is its effects on a persons’ heart health. Stress not only increases a persons' chances of participating in unhealthy activities (eating unhealthily, not exercising due to work load, drinking alcohol, and smoking), it also triggers physiological responses which predisposes a person to heart disease. Chronic stress increases both blood pressure and risk of atherosclerosis (Stress and Cardiovascular disease). Both factors can inevitably lead to heart disease. In addition to heart disease, stress may lead to obesity and diabetes which are both linked to cardiovascular disease in several ways {{citation needed}}.

Other illnesses which stress has been shown to increase the chances of include migraines, ulcers, asthma, infertility, and irritable bowel syndrome. Nearly “75-90% of all doctors visits are due to stress-related ailments (Stress and Cardiovascular disease).” On top of the physical symptoms associated with stress, mental illnesses, such as depression, form as side effects. When the mind cannot keep up with the body, there can be psychological symptoms of distress. Stress shows an important impact on today's society. With the physical and psychological ailments caused by stress, a decreased workload can be able to increase quality of life for American citizens.

== References  ==
* &quot;Stress at Work and How to Manage It&quot;, Arun Bhatia and Rashmi Bhatia, HRM REVIEW,2007, http://www.iupindia.in/1207/HRM_Stress_at_Work_42.html.
* The American Institute of Stress. (n.d.). Retrieved January 20, 2008, from American Institute of Stress Web site: http://www.stress.org/
* Stress on the Brain. (2004). The Human Brain. Retrieved January 20, 2008, from The Frankilin Institute Resources for Science &amp; Learning Web site: http://www.fi.edu/learn/brain/stress.html 
* Stress and Cardiovascular disease. (n.d.). Retrieved January 20, 2008, from Maharishi college of Vedic Medicine Web site: http://www.tm.cme.edu/01.html

== See also ==
{{wikipedia|Stress (biological)}}
* [[Anxiety]]
* [[Coping (psychology)]]

{{psych-stub}}

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  <page>
    <title>Creativity</title>
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      <comment>added discussion question What is creativity?</comment>
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      <text bytes="3661" sha1="6kw3surhl0gmqzz55rkxi36o5c8xdhl" xml:space="preserve">What is creativity? According to [[wikt:creativity|Wiktionary]], creativity is, &quot;The ability to use imagination to produce a novel idea or product that is useful to society&quot;. Here you can learn about creativity, and possibly how to be more creative. 

Creativity — New, valuable ideas!?
{{RightTOC}}
==Discussion questions==
* Can computers be creative? 
* Can artificial intelligence be creative? What is creativity? 
* What are the limits of creativity? Are there any? 

{{Template:design}}
==Techniques==
* [[w:Ideation_(idea_generation)|Ideation (idea generation)]]
* [[w:Dream_journal|Dream journal]]
* [[w:Improvisation|Improvisation]]
* [http://litemind.com/scamper/ SCAMPER]
* [[w:Lateral_thinking|Lateral thinking]]
* [http://www.ted.com/talks/tim_harford.html Trial and Error]
* [[w:Creative problem-solving|Creative problem-solving]]
* And this list of [http://www.mycoted.com/Category:Creativity_Techniques Creativity Techniques] from Mycoted.
==Resources==
* {{cite book |title=A Whack on the Side of the Head: How You Can Be More Creative |last=von Oech |first=Roger   |year=2008 |publisher=Business Plus |isbn=978-0446404662 |pages=256 }}

* {{cite book |title=Thinkertoys: A Handbook of Creative-Thinking Techniques |last=Michalko |first=Michael  |year=2006 |publisher=Ten Speed Press |isbn=978-1580087735 |pages=416 }}
* {{cite book |title=Six Thinking Hats |last=de Bono |first=Edward  |year=1999 |publisher=Back Bay Books |isbn=978-0316178310  |pages=192 }}
* {{cite book |title=The Artist's Way: A Spiritual Path to Higher Creativity |last=Cameron |first=Julia  |year=2002 |publisher=Jeremy P. Tarcher/Putnam |isbn=978-1585421466 |pages=237}}
* {{cite book |title=The New Drawing on the Right Side of the Brain |last=Edwards |first=Betty  |year=1999 |publisher=Tarcher |isbn=978-0874774245 |pages=320}}
* {{cite book |title=Spark: How Creativity Works |last=Burstein |first=Julie |year= 2011 |publisher=Harper |isbn=978-0061732317 |pages= 272 }}
* {{cite book |last=Plucker |first=Jonathan |date=August 1, 2016 |title=Creativity and Innovation: Theory, Research, and Practice |publisher=Prufrock Press |pages=334 |isbn=978-1618215956}}
* Imagine: How Creativity Works
* Koestler's The Act of Creation
* [http://www.ted.com/talks/david_kelley_how_to_build_your_creative_confidence.html How to build your creative confidence], May 2012 TED talk by David Kelley
* [http://www.centerforfutureconsciousness.com/pdf_files/Articles/CreativityWisdomEvolFutureMay2011.pdf Creativity, Wisdom, and Our Evolutionary Future], Thomas Lombardo, Center for Future Consciousness
* Serious Creativity: Using the Power of Lateral Thinking to Create New Ideas
* [http://www.mycoted.com/Category:Creativity_Techniques A to Z of Creativity and Innovation Techniques] is an introduction to a range of tools and techniques for both idea generation (Creativity) and converting those ideas into reality (Innovation).
* Harvest sources from Walter Moss's essay: http://www.wisdompage.com/2014%20Articles/Creative%20and%20Imaginative%20Wisdom.doc
** ''The Act of Creation'', by Arthur Koestler
** ''Handbook of Creativity'', edited by Robert J. Sternberg
** ''How Dogmatic Beliefs Harm Creativity and Higher-Level Thinking'', edited by Robert J. Sternberg and Don Ambrose
* (Evaluate the book: ''Group Genius: The Creative Power of Collaboration''. )
* (Evaluate the book: ''Originals: How Non-Conformists Move the World'', by Adam Grant )
* (Evaluate the book: ''Genius Unmasked'', by Roberta Ness )
* (Evaluate the book: ''Handbook of Creativity'', by Robert J. Sternberg )

==See also==
* [[Creativity/Reading list]]
{{sisterprojectsearch}}
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  <page>
    <title>Open management</title>
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      <comment>==Discussion questions, essay ideas, and learning related AI prompt ideas== * How can open management be applied to decentralized autonomous organizations?</comment>
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'''Open management''' is one of the suggested criteria for [[open academia]], but the principles can apply in any organisation or task/group process.

==See also==
* [[User:Jtneill/Articles/Open management|Open management]] (James Neill, Wikiversity)
* [[w:Transparency_(management)#Management|Transparency (management)#Management]] (Wikipedia)

==Discussion questions, essay ideas, and learning related AI prompt ideas==
* How can open management be applied to decentralized autonomous organizations? 

==External links==
* [http://www.slideshare.net/charleneli/sxsw-open-leadership Open leadership] (Slideshare)

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&lt;div style=&quot;text-align: center;&quot;&gt;''Collaborative online book chapter authoring''
&lt;!-- ---------------------------------- ---&gt;
&lt;!-- Count down --&gt;
&lt;!-- ---------------------------------- ---&gt;&lt;!--
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{{/Contents/}}&lt;/div&gt;
{{TOCright}}

==Overview==
* Weight: 50%
* Due {{/Due}}
* Tasks
** Author an online [[Motivation and emotion/Book|book chapter]] (up to 4,000 words) that explains key psychological theory and research about a unique, specific motivation or emotion topic.
** Develop the chapter by building on the [[Motivation and emotion/Assessment/Topic|topic development]] plan and addressing feedback.
** Contribute to the development of other book chapters (social contribution).
* Follow the [[#Instructions|instructions]] and address the [[#Marking criteria|marking criteria]].

==Purpose==
The purpose of the book chapter is to explain and critically evaluate what psychological science says about a specific motivation or emotion topic, and to demonstrate how this knowledge can be applied to understanding and improving human behaviour in everyday life.

==Marking and feedback==
* Submissions will be marked according to the [[#Marking criteria|marking criteria]] and [https://docs.google.com/document/d/15NXyApC5i6svEcJAnXv9QeRA-cbojy1m8lKReZgBH60/edit?usp=sharing marking rubric].
* Marks will be provided via {{Motivation and emotion/Canvas}} when the university releases unit results (see [https://www.canberra.edu.au/about-uc/key-dates/ Key dates]).
* Up to 5 bonus marks will be awarded in exceptional circumstances where social contributions are above and beyond those required for HD-level (see [https://docs.google.com/document/d/15NXyApC5i6svEcJAnXv9QeRA-cbojy1m8lKReZgBH60 rubric]).
* Written feedback about how well the chapter addresses the marking criteria will be available via the topic's Wikiversity discussion page.
* Follow up with the [[Motivation and emotion/About/Staff|unit convener]] if you have any questions.

==Extensions and late submissions==
* Apply for extension using the unit's online Extension Application Form (see {{Motivation and emotion/Canvas}}) with appropriate documentary evidence.
* Submissions will be accepted up to 3 days late (-10% per day).
* If you don't submit this assessment it is unlikely that you will pass the unit.

==Learning outcomes==
How the unit's [[Motivation and emotion/About/Learning outcomes|learning outcomes]] are addressed by this assessment exercise:
{| border=1 cellpadding=5 cellspacing=&quot;0&quot; background:transparent style=&quot;width:90%; margin: auto; vertical-align:top;&quot;
|-
| style=&quot;width:40%;&quot; | '''Learning outcome'''
| style=&quot;width:60%;&quot; | '''Assessment task'''
|-
| style=&quot;vertical-align:top;&quot; | Integrate theories and current research towards explaining the role of motivation and emotions in human behaviour.
| style=&quot;vertical-align:top;&quot; | Use the most relevant theories and peer-reviewed research to explain a specific motivation or emotion topic.
|-
| style=&quot;vertical-align:top;&quot; | Critically apply knowledge of motivation or emotion to an indepth understanding of a specific topic in this field.
| style=&quot;vertical-align:top;&quot; | Explain how psychological science can be applied to a specific motivation or emotion topic. Use figures, examples, and/or other interactive learning features to illustrate how this knowledge can apply to understanding human behaviour in everyday life.
|}

==Graduate attributes==
How the unit's [[Motivation and emotion/About/Graduate attributes|graduate attributes]] are addressed by this assessment exercise:

{| border=1 cellpadding=5 cellspacing=&quot;0&quot; background:transparent style=&quot;width:90%; margin: auto;&quot;
|-
! style=&quot;width:20%;&quot; | Category
! style=&quot;width:20%;&quot; | Graduate attribute
! style=&quot;width:60%;&quot; | Assessment task
|-
| rowspan=&quot;4&quot; style=&quot;vertical-align:top;&quot; | '''Be professional'''
| style=&quot;vertical-align:top;&quot; | Communicate effectively
| style=&quot;vertical-align:top;&quot; | Review scholarly knowledge in an open, online environment and address feedback.
|-
| style=&quot;vertical-align:top;&quot; | Display initiative and drive
| style=&quot;vertical-align:top;&quot; | Produce an online book chapter about a novel motivation or emotion topic.
|-
| style=&quot;vertical-align:top;&quot; | Up-to-date knowledge and skills
| style=&quot;vertical-align:top;&quot; | Utilise the most relevant psychological theory and research to address a practical question.
|-
| style=&quot;vertical-align:top;&quot; | Solve problems via thinking
| style=&quot;vertical-align:top;&quot; | Use critical thinking to explain how psychological science can address real-world problems.
|-
| rowspan=&quot;3&quot; style=&quot;vertical-align:top;&quot; | '''Be a global citizen'''
| style=&quot;vertical-align:top;&quot; | Informed and balanced
| style=&quot;vertical-align:top;&quot; | Provide a balanced, critical chapter which is accessible to a lay audience.
|-
| style=&quot;vertical-align:top;&quot; | Communicate diversely
| style=&quot;vertical-align:top;&quot; | Collaborate with peers to communicate knowledge openly with a global audience.
|-
| style=&quot;vertical-align:top;&quot; | Creative use of technology
| style=&quot;vertical-align:top;&quot; | Learn how to collaborate using wiki technology.
|-
| rowspan=&quot;2&quot; style=&quot;vertical-align:top;&quot; | '''Be a lifelong learner'''
| style=&quot;vertical-align:top;&quot; | Engage in new ideas
| style=&quot;vertical-align:top;&quot; | Engage in a collaborative learning culture by incorporating feedback and suggestions.
|-
| style=&quot;vertical-align:top;&quot; | Evaluate and adopt new technology
| style=&quot;vertical-align:top;&quot; | Experience project work in a collaborative, online editing environment.
|}

==Instructions==
The book chapter should communicate your understanding of the topic based on the best available psychological theory and research. Explain and apply the most relevant evidence in a clear, engaging, and accessible way. The aim is to demonstrate your ability to synthesise and critically evaluate psychological science in order to understand and respond to a specific motivation or emotion phenomenon.

The following instructions should be used to guide the development of the book chapter.

===Theme===
* Chapters should fit the book theme which is &quot;understanding and improving our motivational and emotional lives using psychological science&quot;

===Audience===
* The target audience is a general (non-topic-expert) reader interested in personal growth and development based on knowledge in psychological science (theory and research). This is a [[w:science communication|science communication]] exercise.

===Wikiversity===
* Present the chapter as a single page on the [[Main Page|English Wikiversity]] website. A link to the chapter should appear in the [[Motivation and emotion/Book|table of contents]] along with the lead author's Wikiversity user name

===Topic===
* The title and sub-title must be approved by the [[Motivation and emotion/About/Staff|unit convener]]

===Collaboration and feedback===
* Chapters should be independently developed and written primarily by the lead author, but collaboration is strongly encouraged (e.g., by incorporating useful edits and feedback from others)
* [[Motivation and emotion/Assessment/Using generative AI|Generative AI]] may be used with appropriate acknowledgement
* Lead authors are encouraged to seek feedback about the chapter during the drafting process (e.g., start a {{Motivation and emotion/Canvas}} discussion thread&lt;!-- (use the chapter title and subtitle in the subject line and include a clickable hyperlink to the chapter in the message)--&gt;)
* Feedback is usually best placed on the chapter's wiki discussion page
* Feedback on the [[Motivation and emotion/Assessment/Topic|topic development]] (chapter plan) will be provided by the [[Motivation and emotion/About/Staff|unit convener]]

===Length (word count)===
{{Anchor|Wordcount}}{{Anchor|Word count}}
* There is no minimum length
* Maximum 4,000 words
** There is no additional 10% allowance
** Words beyond the maximum will not be considered for marking purposes
** Count everything from top to bottom of the editable page (in view mode, not edit mode):
*** Include the title, subtitle, headings, text, tables, figures, references, see also, and external links; don't include menu text across the top and down the left, or categories at the bottom
** How to count:
*** Google Chrome extension: [https://chromewebstore.google.com/detail/word-counter/cbjddaobmdfhbfgdgjocbhklpmclcboe Word Counter]. This extension is probably the easiest reliable method for counting words on a Wikiversity page. However, UC recently started blocking this extension on UC devices.
*** Website: Paste the URL into [https://hsuper.tools/web-page-word-counter Webpage Word Counter] (it overcounts by ~100 words because it includes menus etc.)
*** Word processor: Cut and paste into a word processor (i.e., copy starting at title and finishing with the last external link)
* If the chapter exceeds the maximum word count, see [[/Word count|these suggestions]] for strategies to reduce the length while retaining the key content.

===Submission===
* Submit the chapter URL (website address), your Wikiversity user name, and a PDF of the chapter via {{Motivation and emotion/Canvas}}

==Marking criteria==
[[File:Balanced scales.svg|right|125px]]
Book chapters will be marked against the following criteria.

===Overview (5%)===
* Scenario: Provide an engaging scenario or case study in a feature box, with an illustrative figure
* Problem statement: Easy to read and understand outline of the key concepts and explanation of practical/real-world problem to be solved
* Focus questions: Establish [[/Focus questions|focus questions]] which align with the sub-title and subsequent heading structure

===Theory (20%)===
* Clearly explain the theoretical framework for understanding the topic
* Select the most relevant psychological theories/models that apply to the problem. Depending on the topic, this may involve focusing on a single theory or comparing and contrasting two or more theories.
* Use at least the best dozen or so peer-reviewed theory references about the topic (e.g., see [[Motivation and emotion/Journals|list of motivation and emotion journals)
* Clearly explain and apply the theory(ies)
* Include illustrative examples, such as case studies
* Demonstrate a critical perspective

===Research (25%)===
* Clearly explain how key, peer-reviewed research findings apply to the problem
* Use at least the best dozen or so peer-reviewed research references about the topic (e.g., see [[Motivation and emotion/Journals|list of motivation and emotion journals]])
* Include relevant major reviews (such as systematic reviews and meta-analyses)
* [[w:Critical thinking|Critical analyse]] the key research findings, including limitations and implications

===Integration (10%)===
* Integrate discussion of theory and review of relevant research
* Use research to critically inform interpretation and application of the theory(ies)

===Conclusion (5%)===
* Clear and concise communication of key points and take-home messages
* Aligned with the subtitle and focus questions, with implications for the [[Motivation and emotion/Book/Theme|book theme]]

===Style (20%)===
* Overall
** Present and illustrate the problem and knowledge in an interesting way, using a logical structure, clear layout, correct spelling and grammar, and [[APA style]]
** [[/Readability|Readable]] for a layperson interested in psychological science
** Address the [[#Theme|book theme]] by providing practical, academically sound, self-improvement information
** Address an international audience (i.e., avoid an overly local or national perspective)
** Use default wiki style for paragraph alignment, font colour, type, and size, and heading styles
** Use Australian spelling (e.g., hypothesise, behaviour, fulfilment) rather than American spelling (e.g., hypothesize, behavior, fulfillment)
** Correct grammar (e.g., see [[/Writing tips|writing tips]])
* Structure
** Use a logical heading structure that aligns with the focus questions
** Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] throughout, including for headings and sub-headings
** Use the default heading style (e.g., do not add italics and/or bold)
** Sub-headings are optional
*** Avoid having sections with a single sub-heading — each section should contain 0 or 2+ sub-headings.
*** If sub-headings are used, provides at least 1 introductory paragraph before branching into sub-sections.
* Sentences
** [[w:Narration#Narrative point of view|Narrative point of view]][https://www.grammarly.com/blog/first-second-and-third-person/]: In the main text, use [[w:Narration#Third-person|3rd person perspective]] (e.g., &quot;it&quot;, &quot;they&quot;). Where [[w:Aside|aside]]s are used, such as examples, case studies, and feature boxes, [[w:First-person narrative|1st person perspective]] (e.g., &quot;I&quot; and &quot;we&quot;) and/or [[w:Narration#Second-person|2nd person perspective]] (e.g., &quot;you&quot;) can work well.
* Paragraphs
** A well-constructed paragraph is generally 3 to 5 sentences (opening sentence, body sentences, and a concluding/linking sentence). Avoid one-sentence paragraphs and overly long paragraphs.
** Paragraphs flow logically
* Use APA style (as much as reasonably possible), paying particular attention to:
** citations
** references (especially capitalisation, italicisation, and providing hyperlinked dois)
** table and figure captions
** quotes (include page numbers)
* Citations
** Claims need citations using APA style or [[w:Wikipedia:Citing_sources|wiki citation style]]. Only use one style throughout the chapter — don't mix and match. For most psychology students, APA style will be the choice.
** Maximum of 3 citations per point (i.e., avoid 4 or more citations together).
* References
** List all cited academic references in APA style or [[w:Wikipedia:Citing_sources|wiki citation style]]. Only use one style.
** Non-academic sources are not used in references. They can be included in the external links section.

===Learning features (5%)===
* Embed interactive learning features such as scenarios/case studies/examples, feature boxes, figures, quizzes, links to relevant Wikipedia and Wikipedia pages, as well as links to key resources via the &quot;See also&quot; and &quot;External links&quot; sections
* Case studies
** Include 1 or more examples, scenarios, or case studies
** They can be true (if so, include citations) or fictional
** Use these examples to enhance understanding of theory, research, focus questions, and/or take-home messages
** Present in a feature box and include a figure
** Consider using a &quot;progressive case study&quot; (i.e., a case study presented in separate parts which describe, for example, the problem, attempt at change, and resolution/outcomes).
** Examples of chapters which make effective use of case studies:
*** [[Motivation and emotion/Book/2019/Emotional abuse|emotional abuse]] (2019)
*** [[Motivation and emotion/Book/2019/Food and fear|food and fear]] (2019)
*** [[Motivation and emotion/Book/2019/Opioid system and human emotion|opioid system and human emotion]] (2019)
*** [[Motivation and emotion/Book/2019/Social support and emotion|social support and emotion]] (2019)
* [[Motivation and emotion/Wikiversity/Feature box|Feature boxes]]
** Use to highlight key information, but avoid overuse
** There are various ways of creating coloured boxes, but the [[Template:RoundBoxTop|RoundBox]] template is a good option.
* [[Motivation and emotion/Wikiversity/Figures|Figures]]
** Include relevant, accompanying figures (e.g., photos, drawings, diagrams) to facilitate readers' understanding of the concepts
** Figures are accompanied by explanatory captions and be cited at least once in the main text
** For more information, see [[Motivation and emotion/Assessment/Chapter/Figures|How to use figures]]).
* [[Help:Links|Links]]
** In-text (embedded) links: Key words and concepts are [[Making links|linked]] to Wikipedia articles and/or related book chapters. Provide in-text wiki links the ''first time'' that key concepts are mentioned. For example:
*** [[w:Emotion|emotion]] involves physiological, subjective feeling, motivational, and socially expressive aspects. The syntax for creating this link is &lt;nowiki&gt;[[w:Emotion|emotion]]&lt;/nowiki&gt;). It is also possible to link to a section on this same page e.g., &amp;lt;nowiki&amp;gt;[[#Overview|Overview]]&amp;lt;nowiki&amp;gt; will link to the Overview section.
*** [[Motivation and emotion/Book/2021/Fitspiration and body image|This chapter]] provides an excellent example of embedded links to Wikiversity pages.
** See also
*** Provide interwiki links to key related Wikiversity book chapters and/or Wikipedia articles
*** Include source in parentheses
** External links
*** Provide at least three links to high quality, relevant external resources
*** Include author and/or source in parentheses
** Published academic sources belong in References
* [[Motivation and emotion/Wikiversity/Tables|Tables]]
** Use accompanying tables to help organise information and communicate concepts to readers
** Tables are accompanied by explanatory APA style captions and are cited in the body text
* [[Help:Quiz|Quizzes]]
** Quiz questions or reflection questions encourage reader engagement
** Focus on core concepts (esp. take-home messages) rather than trivia
** Consider incorporating throughout the chapter
{{anchor|Socialcontribution}}

{{anchor|Social contribution}}
===Social contribution (10%)===
* '''Actions''': Logged contributions which enhance the quality of other book chapters. Useful actions include:
** '''Edits''': Direct edits which improve past or current chapters (e.g., fix errors, enhance clarity) or flag potential improvements by adding [[Template:Clarification templates|clarification templates]]. [[/Search for chapters to improve|Search for chapters to improve]].
** '''Comments''': Feedback provided on book chapter [[Help:Talk page|talk page]]s
** '''Media uploads''': Upload free-to-use educational images to [[commons:|Wikimedia Commons]]
** '''{{Motivation and emotion/Canvas}} discussion posts'''
* '''Evidence''':
** Provide a [[mw:Help:Lists|numbered list]] with summaries of contributions on your [[Help:User page|Wikiversity user page]], and '''direct links''' that show each change or contribution.&lt;!-- To receive credit, contributions must be publicly logged (i.e., log in to Wikiversity so that the edit is recorded with your user name and time-stamp). Summarise each edit on your user page (in a section called &quot;Social contributions&quot;) --&gt;
** More info: [[/Summarising social contributions|summarising social contributions]]
* '''Marking'''
** Marking of social contributions will be based on a combination of:
*** '''Quantity''':
**** Breadth: number of chapters contributed to
**** Channels: range of communication channels used
*** '''Quality''':
**** Depth/Extent/Thoroughness
**** Insightfulness
**** Practical value
*** '''Timeliness''' — there is generally:
**** Greater value in earlier contributions
**** Lesser value in last-minute contributions
** Marks will be allocated to each clearly evidenced contribution as follows:
*** Minor &lt;= 0.25
*** Moderate 0.50
*** Major 1.00
*** Very significant &gt; 1.00
* '''Bonus marks'''
** Up to 5 bonus marks (out of 100 for the book chapter) will be awarded in exceptional circumstances where social contributions are above and beyond those required for HD-level.
** Approximately 5% of students receive social contribution bonus marks.
** This could include extensive copyediting of multiple chapters and/or regular feedback or support on multiple chapter discussion pages. It may also involve substantial activity on the UCLearn discussion forum.

==Marking rubric==
{{Notice|1=[https://docs.google.com/document/d/1NUNjMCM5xOVsHj1LJuRnK8BgEdXPn4TbRf-Q6PH3oXg/edit?usp=sharing Marking rubric]}}

==Examples==
Examples of high quality [[Motivation and emotion/Book|motivation and emotion book chapters]]:
* [[Motivation and emotion/Book/2025/AI use, cognitive load, and motivation|AI use, cognitive load, and motivation]] - How does generative AI reduce cognitive effort, and what are the motivational consequences? (2025)
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]]: How does autonomy influence intrinsic motivation according to SDT? (2025)
* [[Motivation and emotion/Book/2022/Disappointment|Disappointment]]: What is disappointment, what causes it, and how can it be managed? (2022)
* [[Motivation and emotion/Book/2016/Illicit drug taking at music festivals|Illicit drug taking at music festivals]]: What motivates young people to take illicit drugs at music festivals? (2016)
* [[Motivation and emotion/Book/2019/Organisational change motivation|Organisational change motivation]]: How can leaders build a culture of agility, adaptability, and resilience to deal with a constantly changing workplace? (2019)
* [[Motivation and emotion/Book/2019/Phobias|Phobias]]: What are phobias and how can they be dealt with? (2019)
* [[Motivation and emotion/Book/2025/Transactive goal dynamics theory and motivation|Transactive goal dynamics theory and motivation]]: What is transactive goal dynamics theory and how does it impact motivation? (2025)

Note that as of 2025, chapters no longer include multimedia presentations.

For more examples, see the {{Motivation and emotion/Book/High}}s in the [[Motivation and emotion/Book|lists of previous book chapters]]&lt;!-- and the [[:Category:Motivation and emotion/Book/2022/Top|top chapters of 2022]] --&gt;.

==Licensing==
Contributions to Wikiversity are made under a [http://creativecommons.org/licenses/by-sa/4.0/ Creative Commons 4.0 Share-alike] (CC-BY-SA 4.0) license which is irrevocable. This license gives permission for others to edit and re-use, with appropriate acknowledgement. For more information, see the [[wmf:Terms of use|Wikimedia Foundation's Terms of use]]. If you do not wish to contribute your work under this license, discuss [[Motivation and emotion/Assessment/Alternative|alternative assessment options]] with the unit convener.

==See also==
* [[/FAQ/]]
* [[Motivation and emotion/Book|Previous chapters]]
* Marking and feedback
** [[Motivation and emotion/Assessment/Chapter/Feedback|General feedback]]
** [[Template:MEBF|Feedback template]]
** [https://docs.google.com/document/d/15NXyApC5i6svEcJAnXv9QeRA-cbojy1m8lKReZgBH60/edit?usp=sharing Marking rubric]
* [[#Socialcontribution|Social contributions]]
** [[/Search for chapters to improve/]]
** [[/Summarising social contributions/]]
* [[Motivation and emotion/Tutorials|Tutorials]]
&lt;!-- ** [[Motivation and emotion/Tutorials/Topic selection|Tutorial 01: Topic selection]] --&gt;
** [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2: Wiki editing]]
** [[Motivation and emotion/Tutorials/Functionalist theory and self-tracking#Google Scholar|Tutorial 5: Google Scholar]]
** [[Motivation and emotion/Tutorials/Measuring emotion#Topic development feedback|Tutorial 8: Topic development feedback]]
* Wikiversity
** [[/Feature boxes/]]
** [[/Figures/]]
** [[How to find free-to-use images|Find free images]]
** [[/Tables/]]
* [[/Writing tips/]]
** [[/How to handle a lack of information/|Handling a lack of information]]
** [[/Readability|Readability]]
** [[Motivation and emotion/Assessment/Using generative AI|Using generative AI]]
** [[/Word count|Word count]]
{{Motivation and emotion/Assessment/Navigation}}
[[Category:Motivation and emotion/Assessment/Chapter| ]]
[[Category:Motivation and emotion guidelines]]</text>
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      <text bytes="23714" sha1="r0zor6uiog9q6g1mfdkt9qajqdn50ca" xml:space="preserve">{{title|Book chapter — Guidelines}}
&lt;div style=&quot;text-align: center;&quot;&gt;''Collaborative online book chapter authoring''
&lt;!-- ---------------------------------- ---&gt;
&lt;!-- Count down --&gt;
&lt;!-- ---------------------------------- ---&gt;&lt;!--
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 |month      = 10
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--&gt;&lt;!-- {{Motivation and emotion/Assessment/In development}} --&gt;
{{/Contents/}}&lt;/div&gt;
{{TOCright}}

==Overview==
* Weight: 50%
* Due {{/Due}}
* Tasks
** Author an online [[Motivation and emotion/Book|book chapter]] (up to 4,000 words) that explains key psychological theory and research about a unique, specific motivation or emotion topic.
** Develop the chapter by building on the [[Motivation and emotion/Assessment/Topic|topic development]] plan and addressing feedback.
** Contribute to the development of other book chapters (social contribution).
* Follow the [[#Instructions|instructions]] and address the [[#Marking criteria|marking criteria]].

==Purpose==
The purpose of the book chapter is to explain and critically evaluate what psychological science says about a specific motivation or emotion topic, and to demonstrate how this knowledge can be applied to understanding and improving human behaviour in everyday life.

==Marking and feedback==
* Submissions will be marked according to the [[#Marking criteria|marking criteria]] and [https://docs.google.com/document/d/15NXyApC5i6svEcJAnXv9QeRA-cbojy1m8lKReZgBH60/edit?usp=sharing marking rubric].
* Marks will be provided via {{Motivation and emotion/Canvas}} when the university releases unit results (see [https://www.canberra.edu.au/about-uc/key-dates/ Key dates]).
* Up to 5 bonus marks will be awarded in exceptional circumstances where social contributions are above and beyond those required for HD-level (see [https://docs.google.com/document/d/15NXyApC5i6svEcJAnXv9QeRA-cbojy1m8lKReZgBH60 rubric]).
* Written feedback about how well the chapter addresses the marking criteria will be available via the topic's Wikiversity discussion page.
* Follow up with the [[Motivation and emotion/About/Staff|unit convener]] if you have any questions.

==Extensions and late submissions==
* Apply for extension using the unit's online Extension Application Form (see {{Motivation and emotion/Canvas}}) with appropriate documentary evidence.
* Submissions will be accepted up to 3 days late (-10% per day).
* If you don't submit this assessment it is unlikely that you will pass the unit.

==Learning outcomes==
How the unit's [[Motivation and emotion/About/Learning outcomes|learning outcomes]] are addressed by this assessment exercise:
{| border=1 cellpadding=5 cellspacing=&quot;0&quot; background:transparent style=&quot;width:90%; margin: auto; vertical-align:top;&quot;
|-
| style=&quot;width:40%;&quot; | '''Learning outcome'''
| style=&quot;width:60%;&quot; | '''Assessment task'''
|-
| style=&quot;vertical-align:top;&quot; | Integrate theories and current research towards explaining the role of motivation and emotions in human behaviour.
| style=&quot;vertical-align:top;&quot; | Use the most relevant theories and peer-reviewed research to explain a specific motivation or emotion topic.
|-
| style=&quot;vertical-align:top;&quot; | Critically apply knowledge of motivation or emotion to an indepth understanding of a specific topic in this field.
| style=&quot;vertical-align:top;&quot; | Explain how psychological science can be applied to a specific motivation or emotion topic. Use figures, examples, and/or other interactive learning features to illustrate how this knowledge can apply to understanding human behaviour in everyday life.
|}

==Graduate attributes==
How the unit's [[Motivation and emotion/About/Graduate attributes|graduate attributes]] are addressed by this assessment exercise:

{| border=1 cellpadding=5 cellspacing=&quot;0&quot; background:transparent style=&quot;width:90%; margin: auto;&quot;
|-
! style=&quot;width:20%;&quot; | Category
! style=&quot;width:20%;&quot; | Graduate attribute
! style=&quot;width:60%;&quot; | Assessment task
|-
| rowspan=&quot;4&quot; style=&quot;vertical-align:top;&quot; | '''Be professional'''
| style=&quot;vertical-align:top;&quot; | Communicate effectively
| style=&quot;vertical-align:top;&quot; | Review scholarly knowledge in an open, online environment and address feedback.
|-
| style=&quot;vertical-align:top;&quot; | Display initiative and drive
| style=&quot;vertical-align:top;&quot; | Produce an online book chapter about a novel motivation or emotion topic.
|-
| style=&quot;vertical-align:top;&quot; | Up-to-date knowledge and skills
| style=&quot;vertical-align:top;&quot; | Utilise the most relevant psychological theory and research to address a practical question.
|-
| style=&quot;vertical-align:top;&quot; | Solve problems via thinking
| style=&quot;vertical-align:top;&quot; | Use critical thinking to explain how psychological science can address real-world problems.
|-
| rowspan=&quot;3&quot; style=&quot;vertical-align:top;&quot; | '''Be a global citizen'''
| style=&quot;vertical-align:top;&quot; | Informed and balanced
| style=&quot;vertical-align:top;&quot; | Provide a balanced, critical chapter which is accessible to a lay audience.
|-
| style=&quot;vertical-align:top;&quot; | Communicate diversely
| style=&quot;vertical-align:top;&quot; | Collaborate with peers to communicate knowledge openly with a global audience.
|-
| style=&quot;vertical-align:top;&quot; | Creative use of technology
| style=&quot;vertical-align:top;&quot; | Learn how to collaborate using wiki technology.
|-
| rowspan=&quot;2&quot; style=&quot;vertical-align:top;&quot; | '''Be a lifelong learner'''
| style=&quot;vertical-align:top;&quot; | Engage in new ideas
| style=&quot;vertical-align:top;&quot; | Engage in a collaborative learning culture by incorporating feedback and suggestions.
|-
| style=&quot;vertical-align:top;&quot; | Evaluate and adopt new technology
| style=&quot;vertical-align:top;&quot; | Experience project work in a collaborative, online editing environment.
|}

==Instructions==
The book chapter should communicate your understanding of the topic based on the best available psychological theory and research. Explain and apply the most relevant evidence in a clear, engaging, and accessible way. The aim is to demonstrate your ability to synthesise and critically evaluate psychological science in order to understand and respond to a specific motivation or emotion phenomenon.

The following instructions should be used to guide the development of the book chapter.

===Theme===
* Chapters should fit the book theme which is &quot;understanding and improving our motivational and emotional lives using psychological science&quot;

===Audience===
* The target audience is a general (non-topic-expert) reader interested in personal growth and development based on knowledge in psychological science (theory and research). This is a [[w:science communication|science communication]] exercise.

===Wikiversity===
* Present the chapter as a single page on the [[Main Page|English Wikiversity]] website. A link to the chapter should appear in the [[Motivation and emotion/Book|table of contents]] along with the lead author's Wikiversity user name

===Topic===
* The title and sub-title must be approved by the [[Motivation and emotion/About/Staff|unit convener]]

===Collaboration and feedback===
* Chapters should be independently developed and written primarily by the lead author, but collaboration is strongly encouraged (e.g., by incorporating useful edits and feedback from others)
* [[Motivation and emotion/Assessment/Using generative AI|Generative AI]] may be used with appropriate acknowledgement
* Lead authors are encouraged to seek feedback about the chapter during the drafting process (e.g., start a {{Motivation and emotion/Canvas}} discussion thread&lt;!-- (use the chapter title and subtitle in the subject line and include a clickable hyperlink to the chapter in the message)--&gt;)
* Feedback is usually best placed on the chapter's wiki discussion page
* Feedback on the [[Motivation and emotion/Assessment/Topic|topic development]] (chapter plan) will be provided by the [[Motivation and emotion/About/Staff|unit convener]]

===Length (word count)===
{{Anchor|Wordcount}}{{Anchor|Word count}}
* There is no minimum length
* Maximum 4,000 words
** There is no additional 10% allowance
** Words beyond the maximum will not be considered for marking purposes
** Count everything from top to bottom of the editable page (in view mode, not edit mode):
*** Include the title, subtitle, headings, text, tables, figures, references, see also, and external links; don't include menu text across the top and down the left, or categories at the bottom
** How to count:
*** Google Chrome extension: [https://chromewebstore.google.com/detail/word-counter/cbjddaobmdfhbfgdgjocbhklpmclcboe Word Counter]. This extension is probably the easiest reliable method for counting words on a Wikiversity page. However, UC recently started blocking this extension on UC devices.
*** Website: Paste the URL into [https://hsuper.tools/web-page-word-counter Webpage Word Counter] (it overcounts by ~100 words because it includes menus etc.)
*** Word processor: Cut and paste into a word processor (i.e., copy starting at title and finishing with the last external link)
* If the chapter exceeds the maximum word count, see [[/Word count|these suggestions]] for strategies to reduce the length while retaining the key content.

===Submission===
* Submit the chapter URL (website address), your Wikiversity user name, and a PDF of the chapter via {{Motivation and emotion/Canvas}}

==Marking criteria==
[[File:Balanced scales.svg|right|125px]]
Book chapters will be marked against the following criteria.

===Overview (5%)===
* Scenario: Provide an engaging scenario or case study in a feature box, with an illustrative figure
* Problem statement: Easy to read and understand outline of the key concepts and explanation of practical/real-world problem to be solved
* Focus questions: Establish [[/Focus questions|focus questions]] which align with the sub-title and subsequent heading structure

===Theory (20%)===
* Clearly explain the theoretical framework for understanding the topic
* Select the most relevant psychological theories/models that apply to the problem. Depending on the topic, this may involve focusing on a single theory or comparing and contrasting two or more theories.
* Use at least the best dozen or so peer-reviewed theory references about the topic (e.g., see [[Motivation and emotion/Journals|list of motivation and emotion journals]])
* Clearly explain and apply the theory(ies)
* Include illustrative examples, such as case studies
* Demonstrate a critical perspective

===Research (25%)===
* Clearly explain how key, peer-reviewed research findings apply to the problem
* Use at least the best dozen or so peer-reviewed research references about the topic (e.g., see [[Motivation and emotion/Journals|list of motivation and emotion journals]])
* Include relevant major reviews (such as systematic reviews and meta-analyses)
* [[w:Critical thinking|Critical analyse]] the key research findings, including limitations and implications

===Integration (10%)===
* Integrate discussion of theory and review of relevant research
* Use research to critically inform interpretation and application of the theory(ies)

===Conclusion (5%)===
* Clear and concise communication of key points and take-home messages
* Aligned with the subtitle and focus questions, with implications for the [[Motivation and emotion/Book/Theme|book theme]]

===Style (20%)===
* Overall
** Present and illustrate the problem and knowledge in an interesting way, using a logical structure, clear layout, correct spelling and grammar, and [[APA style]]
** [[/Readability|Readable]] for a layperson interested in psychological science
** Address the [[#Theme|book theme]] by providing practical, academically sound, self-improvement information
** Address an international audience (i.e., avoid an overly local or national perspective)
** Use default wiki style for paragraph alignment, font colour, type, and size, and heading styles
** Use Australian spelling (e.g., hypothesise, behaviour, fulfilment) rather than American spelling (e.g., hypothesize, behavior, fulfillment)
** Correct grammar (e.g., see [[/Writing tips|writing tips]])
* Structure
** Use a logical heading structure that aligns with the focus questions
** Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] throughout, including for headings and sub-headings
** Use the default heading style (e.g., do not add italics and/or bold)
** Sub-headings are optional
*** Avoid having sections with a single sub-heading — each section should contain 0 or 2+ sub-headings.
*** If sub-headings are used, provides at least 1 introductory paragraph before branching into sub-sections.
* Sentences
** [[w:Narration#Narrative point of view|Narrative point of view]][https://www.grammarly.com/blog/first-second-and-third-person/]: In the main text, use [[w:Narration#Third-person|3rd person perspective]] (e.g., &quot;it&quot;, &quot;they&quot;). Where [[w:Aside|aside]]s are used, such as examples, case studies, and feature boxes, [[w:First-person narrative|1st person perspective]] (e.g., &quot;I&quot; and &quot;we&quot;) and/or [[w:Narration#Second-person|2nd person perspective]] (e.g., &quot;you&quot;) can work well.
* Paragraphs
** A well-constructed paragraph is generally 3 to 5 sentences (opening sentence, body sentences, and a concluding/linking sentence). Avoid one-sentence paragraphs and overly long paragraphs.
** Paragraphs flow logically
* Use APA style (as much as reasonably possible), paying particular attention to:
** citations
** references (especially capitalisation, italicisation, and providing hyperlinked dois)
** table and figure captions
** quotes (include page numbers)
* Citations
** Claims need citations using APA style or [[w:Wikipedia:Citing_sources|wiki citation style]]. Only use one style throughout the chapter — don't mix and match. For most psychology students, APA style will be the choice.
** Maximum of 3 citations per point (i.e., avoid 4 or more citations together).
* References
** List all cited academic references in APA style or [[w:Wikipedia:Citing_sources|wiki citation style]]. Only use one style.
** Non-academic sources are not used in references. They can be included in the external links section.

===Learning features (5%)===
* Embed interactive learning features such as scenarios/case studies/examples, feature boxes, figures, quizzes, links to relevant Wikipedia and Wikipedia pages, as well as links to key resources via the &quot;See also&quot; and &quot;External links&quot; sections
* Case studies
** Include 1 or more examples, scenarios, or case studies
** They can be true (if so, include citations) or fictional
** Use these examples to enhance understanding of theory, research, focus questions, and/or take-home messages
** Present in a feature box and include a figure
** Consider using a &quot;progressive case study&quot; (i.e., a case study presented in separate parts which describe, for example, the problem, attempt at change, and resolution/outcomes).
** Examples of chapters which make effective use of case studies:
*** [[Motivation and emotion/Book/2019/Emotional abuse|emotional abuse]] (2019)
*** [[Motivation and emotion/Book/2019/Food and fear|food and fear]] (2019)
*** [[Motivation and emotion/Book/2019/Opioid system and human emotion|opioid system and human emotion]] (2019)
*** [[Motivation and emotion/Book/2019/Social support and emotion|social support and emotion]] (2019)
* [[Motivation and emotion/Wikiversity/Feature box|Feature boxes]]
** Use to highlight key information, but avoid overuse
** There are various ways of creating coloured boxes, but the [[Template:RoundBoxTop|RoundBox]] template is a good option.
* [[Motivation and emotion/Wikiversity/Figures|Figures]]
** Include relevant, accompanying figures (e.g., photos, drawings, diagrams) to facilitate readers' understanding of the concepts
** Figures are accompanied by explanatory captions and be cited at least once in the main text
** For more information, see [[Motivation and emotion/Assessment/Chapter/Figures|How to use figures]]).
* [[Help:Links|Links]]
** In-text (embedded) links: Key words and concepts are [[Making links|linked]] to Wikipedia articles and/or related book chapters. Provide in-text wiki links the ''first time'' that key concepts are mentioned. For example:
*** [[w:Emotion|emotion]] involves physiological, subjective feeling, motivational, and socially expressive aspects. The syntax for creating this link is &lt;nowiki&gt;[[w:Emotion|emotion]]&lt;/nowiki&gt;). It is also possible to link to a section on this same page e.g., &amp;lt;nowiki&amp;gt;[[#Overview|Overview]]&amp;lt;nowiki&amp;gt; will link to the Overview section.
*** [[Motivation and emotion/Book/2021/Fitspiration and body image|This chapter]] provides an excellent example of embedded links to Wikiversity pages.
** See also
*** Provide interwiki links to key related Wikiversity book chapters and/or Wikipedia articles
*** Include source in parentheses
** External links
*** Provide at least three links to high quality, relevant external resources
*** Include author and/or source in parentheses
** Published academic sources belong in References
* [[Motivation and emotion/Wikiversity/Tables|Tables]]
** Use accompanying tables to help organise information and communicate concepts to readers
** Tables are accompanied by explanatory APA style captions and are cited in the body text
* [[Help:Quiz|Quizzes]]
** Quiz questions or reflection questions encourage reader engagement
** Focus on core concepts (esp. take-home messages) rather than trivia
** Consider incorporating throughout the chapter
{{anchor|Socialcontribution}}

{{anchor|Social contribution}}
===Social contribution (10%)===
* '''Actions''': Logged contributions which enhance the quality of other book chapters. Useful actions include:
** '''Edits''': Direct edits which improve past or current chapters (e.g., fix errors, enhance clarity) or flag potential improvements by adding [[Template:Clarification templates|clarification templates]]. [[/Search for chapters to improve|Search for chapters to improve]].
** '''Comments''': Feedback provided on book chapter [[Help:Talk page|talk page]]s
** '''Media uploads''': Upload free-to-use educational images to [[commons:|Wikimedia Commons]]
** '''{{Motivation and emotion/Canvas}} discussion posts'''
* '''Evidence''':
** Provide a [[mw:Help:Lists|numbered list]] with summaries of contributions on your [[Help:User page|Wikiversity user page]], and '''direct links''' that show each change or contribution.&lt;!-- To receive credit, contributions must be publicly logged (i.e., log in to Wikiversity so that the edit is recorded with your user name and time-stamp). Summarise each edit on your user page (in a section called &quot;Social contributions&quot;) --&gt;
** More info: [[/Summarising social contributions|summarising social contributions]]
* '''Marking'''
** Marking of social contributions will be based on a combination of:
*** '''Quantity''':
**** Breadth: number of chapters contributed to
**** Channels: range of communication channels used
*** '''Quality''':
**** Depth/Extent/Thoroughness
**** Insightfulness
**** Practical value
*** '''Timeliness''' — there is generally:
**** Greater value in earlier contributions
**** Lesser value in last-minute contributions
** Marks will be allocated to each clearly evidenced contribution as follows:
*** Minor &lt;= 0.25
*** Moderate 0.50
*** Major 1.00
*** Very significant &gt; 1.00
* '''Bonus marks'''
** Up to 5 bonus marks (out of 100 for the book chapter) will be awarded in exceptional circumstances where social contributions are above and beyond those required for HD-level.
** Approximately 5% of students receive social contribution bonus marks.
** This could include extensive copyediting of multiple chapters and/or regular feedback or support on multiple chapter discussion pages. It may also involve substantial activity on the UCLearn discussion forum.

==Marking rubric==
{{Notice|1=[https://docs.google.com/document/d/1NUNjMCM5xOVsHj1LJuRnK8BgEdXPn4TbRf-Q6PH3oXg/edit?usp=sharing Marking rubric]}}

==Examples==
Examples of high quality [[Motivation and emotion/Book|motivation and emotion book chapters]]:
* [[Motivation and emotion/Book/2025/AI use, cognitive load, and motivation|AI use, cognitive load, and motivation]] - How does generative AI reduce cognitive effort, and what are the motivational consequences? (2025)
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]]: How does autonomy influence intrinsic motivation according to SDT? (2025)
* [[Motivation and emotion/Book/2022/Disappointment|Disappointment]]: What is disappointment, what causes it, and how can it be managed? (2022)
* [[Motivation and emotion/Book/2016/Illicit drug taking at music festivals|Illicit drug taking at music festivals]]: What motivates young people to take illicit drugs at music festivals? (2016)
* [[Motivation and emotion/Book/2019/Organisational change motivation|Organisational change motivation]]: How can leaders build a culture of agility, adaptability, and resilience to deal with a constantly changing workplace? (2019)
* [[Motivation and emotion/Book/2019/Phobias|Phobias]]: What are phobias and how can they be dealt with? (2019)
* [[Motivation and emotion/Book/2025/Transactive goal dynamics theory and motivation|Transactive goal dynamics theory and motivation]]: What is transactive goal dynamics theory and how does it impact motivation? (2025)

Note that as of 2025, chapters no longer include multimedia presentations.

For more examples, see the {{Motivation and emotion/Book/High}}s in the [[Motivation and emotion/Book|lists of previous book chapters]]&lt;!-- and the [[:Category:Motivation and emotion/Book/2022/Top|top chapters of 2022]] --&gt;.

==Licensing==
Contributions to Wikiversity are made under a [http://creativecommons.org/licenses/by-sa/4.0/ Creative Commons 4.0 Share-alike] (CC-BY-SA 4.0) license which is irrevocable. This license gives permission for others to edit and re-use, with appropriate acknowledgement. For more information, see the [[wmf:Terms of use|Wikimedia Foundation's Terms of use]]. If you do not wish to contribute your work under this license, discuss [[Motivation and emotion/Assessment/Alternative|alternative assessment options]] with the unit convener.

==See also==
* [[/FAQ/]]
* [[Motivation and emotion/Book|Previous chapters]]
* Marking and feedback
** [[Motivation and emotion/Assessment/Chapter/Feedback|General feedback]]
** [[Template:MEBF|Feedback template]]
** [https://docs.google.com/document/d/15NXyApC5i6svEcJAnXv9QeRA-cbojy1m8lKReZgBH60/edit?usp=sharing Marking rubric]
* [[#Socialcontribution|Social contributions]]
** [[/Search for chapters to improve/]]
** [[/Summarising social contributions/]]
* [[Motivation and emotion/Tutorials|Tutorials]]
&lt;!-- ** [[Motivation and emotion/Tutorials/Topic selection|Tutorial 01: Topic selection]] --&gt;
** [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2: Wiki editing]]
** [[Motivation and emotion/Tutorials/Functionalist theory and self-tracking#Google Scholar|Tutorial 5: Google Scholar]]
** [[Motivation and emotion/Tutorials/Measuring emotion#Topic development feedback|Tutorial 8: Topic development feedback]]
* Wikiversity
** [[/Feature boxes/]]
** [[/Figures/]]
** [[How to find free-to-use images|Find free images]]
** [[/Tables/]]
* [[/Writing tips/]]
** [[/How to handle a lack of information/|Handling a lack of information]]
** [[/Readability|Readability]]
** [[Motivation and emotion/Assessment/Using generative AI|Using generative AI]]
** [[/Word count|Word count]]
{{Motivation and emotion/Assessment/Navigation}}
[[Category:Motivation and emotion/Assessment/Chapter| ]]
[[Category:Motivation and emotion guidelines]]</text>
      <sha1>r0zor6uiog9q6g1mfdkt9qajqdn50ca</sha1>
    </revision>
  </page>
  <page>
    <title>The necessities in Numerical Methods</title>
    <ns>0</ns>
    <id>119778</id>
    <revision>
      <id>2833708</id>
      <parentid>2833194</parentid>
      <timestamp>2026-09-18T06:27:32Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Non-linear Equations */</comment>
      <origin>2833708</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2914" sha1="4tc9jbk4s5rmpdbgklpvxfief6gcmo1" xml:space="preserve">== Calculus == 
=== Numerical Differentiation ===
* Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]])
* Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]])
* Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241116.pdf |pdf]])
* Forward, Backward, Central Divided Difference
* High Accuracy Differentiation
* Richardson Extrapolation
* Unequal Spaced Data Differentiation
* Numerical Differentiation with Octave
&lt;/br&gt;

=== Non-linear Equations ===
* Bisection Method ([[Media:NM.NLE.1Bisection.20241130.pdf |pdf]])
* Newton-Raphson Method ([[Media:NM.NLE.2Newton.20260915.pdf |pdf]])
* Secant Method
* False-Position Method
&lt;/br&gt;

=== Numerical Integration ===
* Trapezoidal Rule
* Simpson's 1/3 Rule
* Romberg Rule
* Gauss-Quadrature Rule
* Adaptive Quadrature
&lt;/br&gt;

=== Roots of a Nonlinear Equation ===
&lt;/br&gt;

=== Optimization ===
&lt;/br&gt;
&lt;/br&gt;

== Matrix Algebra == 

=== Simultaneous Linear Equations === 
* A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]])


&lt;/br&gt;

=== Gaussian Elimination === 
&lt;/br&gt;

=== LU Decomposition === 
&lt;/br&gt;

=== Cholesky Decomposition === 
&lt;/br&gt;

=== LDL Decomposition === 
&lt;/br&gt;

=== Gauss-Seidel method === 
&lt;/br&gt;

=== Adequacy of Solutions === 
&lt;/br&gt;

=== Eigenvalue and Singular Value ===
&lt;/br&gt;

=== QRD ===
&lt;/br&gt;

=== SVD ===
&lt;/br&gt;

=== Iterative methods ===
&lt;/br&gt;
&lt;/br&gt;

== Regression ==

=== Linear Regression ===
&lt;/br&gt;

=== Non-linear Regression ===
&lt;/br&gt;

=== Linear Least Squares ===
&lt;/br&gt;
&lt;/br&gt; 


== Interpolation ==

=== Polynomial Interpolation ===
&lt;/br&gt;

=== Linear Splines ===
&lt;/br&gt;

=== Piecewise Interpolation ===
&lt;/br&gt;
&lt;/br&gt; 


== Ordinary Differential Equation ==
&lt;/br&gt;

== Partial Differential Equation ==
&lt;/br&gt;

== FEM (Finite Element Method) ==
&lt;/br&gt;
&lt;/br&gt; 


&lt;/br&gt;


== Using Symbolic Package in Octave ==

* Visit http://octave.sourceforge.net/index.html
* Download symbolic-1.0.9.tar.gz

* In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed.

* After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.
 ./configure 
 ./make 
 ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 

* While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu.

== Read some tutorials about symbolic computation ==

* Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf)

* Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf)

[[Category:Numerical methods]]

== Using SymPy ( a Python library for symbolic mathematics) == 
&lt;/br&gt;


&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]</text>
      <sha1>4tc9jbk4s5rmpdbgklpvxfief6gcmo1</sha1>
    </revision>
    <revision>
      <id>2833710</id>
      <parentid>2833708</parentid>
      <timestamp>2026-09-18T06:28:38Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Non-linear Equations */</comment>
      <origin>2833710</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2914" sha1="93zo5kasasl62zw8catbdj6xxuo3mdb" xml:space="preserve">== Calculus == 
=== Numerical Differentiation ===
* Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]])
* Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]])
* Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241116.pdf |pdf]])
* Forward, Backward, Central Divided Difference
* High Accuracy Differentiation
* Richardson Extrapolation
* Unequal Spaced Data Differentiation
* Numerical Differentiation with Octave
&lt;/br&gt;

=== Non-linear Equations ===
* Bisection Method ([[Media:NM.NLE.1Bisection.20241130.pdf |pdf]])
* Newton-Raphson Method ([[Media:NM.NLE.2Newton.20260916.pdf |pdf]])
* Secant Method
* False-Position Method
&lt;/br&gt;

=== Numerical Integration ===
* Trapezoidal Rule
* Simpson's 1/3 Rule
* Romberg Rule
* Gauss-Quadrature Rule
* Adaptive Quadrature
&lt;/br&gt;

=== Roots of a Nonlinear Equation ===
&lt;/br&gt;

=== Optimization ===
&lt;/br&gt;
&lt;/br&gt;

== Matrix Algebra == 

=== Simultaneous Linear Equations === 
* A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]])


&lt;/br&gt;

=== Gaussian Elimination === 
&lt;/br&gt;

=== LU Decomposition === 
&lt;/br&gt;

=== Cholesky Decomposition === 
&lt;/br&gt;

=== LDL Decomposition === 
&lt;/br&gt;

=== Gauss-Seidel method === 
&lt;/br&gt;

=== Adequacy of Solutions === 
&lt;/br&gt;

=== Eigenvalue and Singular Value ===
&lt;/br&gt;

=== QRD ===
&lt;/br&gt;

=== SVD ===
&lt;/br&gt;

=== Iterative methods ===
&lt;/br&gt;
&lt;/br&gt;

== Regression ==

=== Linear Regression ===
&lt;/br&gt;

=== Non-linear Regression ===
&lt;/br&gt;

=== Linear Least Squares ===
&lt;/br&gt;
&lt;/br&gt; 


== Interpolation ==

=== Polynomial Interpolation ===
&lt;/br&gt;

=== Linear Splines ===
&lt;/br&gt;

=== Piecewise Interpolation ===
&lt;/br&gt;
&lt;/br&gt; 


== Ordinary Differential Equation ==
&lt;/br&gt;

== Partial Differential Equation ==
&lt;/br&gt;

== FEM (Finite Element Method) ==
&lt;/br&gt;
&lt;/br&gt; 


&lt;/br&gt;


== Using Symbolic Package in Octave ==

* Visit http://octave.sourceforge.net/index.html
* Download symbolic-1.0.9.tar.gz

* In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed.

* After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.
 ./configure 
 ./make 
 ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 

* While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu.

== Read some tutorials about symbolic computation ==

* Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf)

* Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf)

[[Category:Numerical methods]]

== Using SymPy ( a Python library for symbolic mathematics) == 
&lt;/br&gt;


&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]</text>
      <sha1>93zo5kasasl62zw8catbdj6xxuo3mdb</sha1>
    </revision>
    <revision>
      <id>2833712</id>
      <parentid>2833710</parentid>
      <timestamp>2026-09-18T06:29:28Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Non-linear Equations */</comment>
      <origin>2833712</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2914" sha1="7pzlz2t77sy549b17l0g34xw04f5yei" xml:space="preserve">== Calculus == 
=== Numerical Differentiation ===
* Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]])
* Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]])
* Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241116.pdf |pdf]])
* Forward, Backward, Central Divided Difference
* High Accuracy Differentiation
* Richardson Extrapolation
* Unequal Spaced Data Differentiation
* Numerical Differentiation with Octave
&lt;/br&gt;

=== Non-linear Equations ===
* Bisection Method ([[Media:NM.NLE.1Bisection.20241130.pdf |pdf]])
* Newton-Raphson Method ([[Media:NM.NLE.2Newton.20260917.pdf |pdf]])
* Secant Method
* False-Position Method
&lt;/br&gt;

=== Numerical Integration ===
* Trapezoidal Rule
* Simpson's 1/3 Rule
* Romberg Rule
* Gauss-Quadrature Rule
* Adaptive Quadrature
&lt;/br&gt;

=== Roots of a Nonlinear Equation ===
&lt;/br&gt;

=== Optimization ===
&lt;/br&gt;
&lt;/br&gt;

== Matrix Algebra == 

=== Simultaneous Linear Equations === 
* A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]])


&lt;/br&gt;

=== Gaussian Elimination === 
&lt;/br&gt;

=== LU Decomposition === 
&lt;/br&gt;

=== Cholesky Decomposition === 
&lt;/br&gt;

=== LDL Decomposition === 
&lt;/br&gt;

=== Gauss-Seidel method === 
&lt;/br&gt;

=== Adequacy of Solutions === 
&lt;/br&gt;

=== Eigenvalue and Singular Value ===
&lt;/br&gt;

=== QRD ===
&lt;/br&gt;

=== SVD ===
&lt;/br&gt;

=== Iterative methods ===
&lt;/br&gt;
&lt;/br&gt;

== Regression ==

=== Linear Regression ===
&lt;/br&gt;

=== Non-linear Regression ===
&lt;/br&gt;

=== Linear Least Squares ===
&lt;/br&gt;
&lt;/br&gt; 


== Interpolation ==

=== Polynomial Interpolation ===
&lt;/br&gt;

=== Linear Splines ===
&lt;/br&gt;

=== Piecewise Interpolation ===
&lt;/br&gt;
&lt;/br&gt; 


== Ordinary Differential Equation ==
&lt;/br&gt;

== Partial Differential Equation ==
&lt;/br&gt;

== FEM (Finite Element Method) ==
&lt;/br&gt;
&lt;/br&gt; 


&lt;/br&gt;


== Using Symbolic Package in Octave ==

* Visit http://octave.sourceforge.net/index.html
* Download symbolic-1.0.9.tar.gz

* In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed.

* After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.
 ./configure 
 ./make 
 ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 

* While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu.

== Read some tutorials about symbolic computation ==

* Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf)

* Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf)

[[Category:Numerical methods]]

== Using SymPy ( a Python library for symbolic mathematics) == 
&lt;/br&gt;


&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]</text>
      <sha1>7pzlz2t77sy549b17l0g34xw04f5yei</sha1>
    </revision>
    <revision>
      <id>2833714</id>
      <parentid>2833712</parentid>
      <timestamp>2026-09-18T06:30:18Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Non-linear Equations */</comment>
      <origin>2833714</origin>
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      <format>text/x-wiki</format>
      <text bytes="2914" sha1="q0vk7e4z9vy584dcoz6dysl6eiztize" xml:space="preserve">== Calculus == 
=== Numerical Differentiation ===
* Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]])
* Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]])
* Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241116.pdf |pdf]])
* Forward, Backward, Central Divided Difference
* High Accuracy Differentiation
* Richardson Extrapolation
* Unequal Spaced Data Differentiation
* Numerical Differentiation with Octave
&lt;/br&gt;

=== Non-linear Equations ===
* Bisection Method ([[Media:NM.NLE.1Bisection.20241130.pdf |pdf]])
* Newton-Raphson Method ([[Media:NM.NLE.2Newton.20260918.pdf |pdf]])
* Secant Method
* False-Position Method
&lt;/br&gt;

=== Numerical Integration ===
* Trapezoidal Rule
* Simpson's 1/3 Rule
* Romberg Rule
* Gauss-Quadrature Rule
* Adaptive Quadrature
&lt;/br&gt;

=== Roots of a Nonlinear Equation ===
&lt;/br&gt;

=== Optimization ===
&lt;/br&gt;
&lt;/br&gt;

== Matrix Algebra == 

=== Simultaneous Linear Equations === 
* A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]])


&lt;/br&gt;

=== Gaussian Elimination === 
&lt;/br&gt;

=== LU Decomposition === 
&lt;/br&gt;

=== Cholesky Decomposition === 
&lt;/br&gt;

=== LDL Decomposition === 
&lt;/br&gt;

=== Gauss-Seidel method === 
&lt;/br&gt;

=== Adequacy of Solutions === 
&lt;/br&gt;

=== Eigenvalue and Singular Value ===
&lt;/br&gt;

=== QRD ===
&lt;/br&gt;

=== SVD ===
&lt;/br&gt;

=== Iterative methods ===
&lt;/br&gt;
&lt;/br&gt;

== Regression ==

=== Linear Regression ===
&lt;/br&gt;

=== Non-linear Regression ===
&lt;/br&gt;

=== Linear Least Squares ===
&lt;/br&gt;
&lt;/br&gt; 


== Interpolation ==

=== Polynomial Interpolation ===
&lt;/br&gt;

=== Linear Splines ===
&lt;/br&gt;

=== Piecewise Interpolation ===
&lt;/br&gt;
&lt;/br&gt; 


== Ordinary Differential Equation ==
&lt;/br&gt;

== Partial Differential Equation ==
&lt;/br&gt;

== FEM (Finite Element Method) ==
&lt;/br&gt;
&lt;/br&gt; 


&lt;/br&gt;


== Using Symbolic Package in Octave ==

* Visit http://octave.sourceforge.net/index.html
* Download symbolic-1.0.9.tar.gz

* In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed.

* After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.
 ./configure 
 ./make 
 ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 

* While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu.

== Read some tutorials about symbolic computation ==

* Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf)

* Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf)

[[Category:Numerical methods]]

== Using SymPy ( a Python library for symbolic mathematics) == 
&lt;/br&gt;


&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]</text>
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    <title>User:Marshallsumter/Radiation astronomy/Yellows</title>
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      <contributor>
        <username>CommonsDelinker</username>
        <id>9184</id>
      </contributor>
      <comment>Removing [[:c:File:Krishna.jpg|Krishna.jpg]], it has been deleted from Commons by [[:c:User:Túrelio|Túrelio]] because: [[:c:COM:L|Copyright violation]]: https://factoriahistorica.wordpress.com/2012/04/14/la-antropologia/.</comment>
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      <text bytes="116107" sha1="dluzvxj4ge4lpj9famvpgr9qmpjdb7z" xml:space="preserve">[[Image:Io highest resolution true color.jpg|thumb|right|250px|This is a true-color image of Io taken by the ''Galileo'' probe. Credit: NASA.{{tlx|free media}}]]
'''Yellow astronomy''' is astronomy applied to the various extraterrestrial yellow sources of radiation, especially at night. It is also conducted above the Earth's atmosphere and at locations away from the Earth as a part of explorational (or exploratory) yellow astronomy.

Seeing the yellow [[Stars/Sun|Sun]] and feeling the warmth of its rays is probably a student's first encounter with an astronomical yellow radiation source.

There are yellow objects and emission lines in the yellow portion of the visible spectrum from 570 to 590 nm in wavelength.
{{clear}}

==Anasazi astronomy==
[[Image:Fajadadiagram.JPG|thumb|right|250px|Diagram shows the location of the sun daggers on the petroglyph on various days. Credit: [[w:user:Nationalparks|Nationalparks]].{{tlx|free media}}]]
&quot;When they [the Anasazi] built the kiva, they first put up beams of four different trees. These were the trees that were planted in the underworld for the people to climb up on. In the north, under the foundation they placed yellow turquoise; in the west, blue turquoise, in the south, red, and in the east, white turquoise.&quot;&lt;ref name=&quot;Malville&quot;&gt;{{cite book
|author=J. McKim Malville and Claudia Putnam
|title=Prehistoric Astronomy in the Southwest
|publisher=Big Earth Publishing
|location=Boulder, CO, USA
|date=1993
|editor=
|pages=108
|url=http://books.google.com/books?id=7qRpuKG6xVQC&amp;source=gbs_navlinks_s
|arxiv=
|bibcode=
|doi=
|pmid=
|isbn=1555661165
|accessdate=2013-09-12 }}&lt;/ref&gt;

&quot;The rising of the moon [on the morning of August 8, 1988. The moon's declination was 28.5°.] between the chimneys [of the kiva] is visible from the Chimney Rock Pueblo only at the times of major northern standstill occurring every 18.61 years.&quot;&lt;ref name=&quot;Malville&quot;/&gt;
{{clear}}

==Radiation==
{{main|Radiation}}
{| class=&quot;wikitable&quot; style=&quot;float:right; width:400px; text-align:center; margin:0.5em auto; width:auto; margin-left:1em;&quot;
|-
! colspan=&quot;3&quot; style=&quot;background:#FFF;&quot; | [[Image:Linear visible spectrum.svg|center|250px|sRGB rendering of the spectrum of visible light]]
|-
!Color
|[[Frequency]]
|[[Wavelength]]
|-
| style=&quot;background:#ccb0f4;&quot;|'''[[w:violet (color)|violet]]'''
|668–789&amp;nbsp;THz
|380–450&amp;nbsp;nm
|-
| style=&quot;background:#b0b0f4;&quot;|'''[[w:Blue|blue]]'''
|631–668&amp;nbsp;THz
|450–475&amp;nbsp;nm
|-
| style=&quot;background:#b0f4f4;&quot;|'''[[w:Cyan|cyan]]'''
|606–630&amp;nbsp;THz
|476–495&amp;nbsp;nm
|-
| style=&quot;background:#b0f4b0;&quot;|'''[[w:Green|green]]'''
|526–606&amp;nbsp;THz
|495–570&amp;nbsp;nm
|-
| style=&quot;background:#f4f4b0;&quot;|'''[[w:Yellow|yellow]]'''
|508–526&amp;nbsp;THz
|570–590&amp;nbsp;nm
|-
| style=&quot;background:#f4ccb0;&quot;|'''[[w:orange (color)|orange]]'''
|484–508&amp;nbsp;THz
|590–620&amp;nbsp;nm
|-
| style=&quot;background:#f4b0b0;&quot;|'''[[w:Red|red]]'''
|400–484&amp;nbsp;THz
|620–750&amp;nbsp;nm
|}

&quot;To see day objects with most distinctness, I require a less concave lens by one degree than for seeing the stars best by night, the cause of which seems to be, that the bottom of the eye being illuminated by the day objects, and thereby rendered a light ground, obscures the fainter colours blue indigo and violet in the circle of dissipation, and therefore the best image of the object will be found in the focus of the bright '''yellow rays''', and not in that of the mean refrangible ones, or the dark green, agreeable to Newton's remark, and consequently nearer the retina of a short-sighted person; but the parts of the retina surrounding the circle of dissipation of a star being in the dark, the fainter colours, blue, indigo, and violet, will have some share in forming the image, and consequently the focus will be shorter.&quot;&lt;ref name=&quot;Maskelyne&quot;&gt;{{cite journal
|author=Nevil Maskelyne
|title=An Attempt to Explain a Difficulty in the Theory of Vision, Depending on the Different Refrangibility of Light
|journal=Philosophical Transactions of the Royal Society of London
|date=June 18 1789
|volume=79
|issue=
|pages=256-64
|url=http://www.jstor.org/stable/106696
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2013-09-13 }}&lt;/ref&gt; Bold added.

&quot;The error due to color loses its disturbing effect because the photographic plate is not sensitive for the red and yellow rays, while the photographically active rays of shorter wave-length are well united by the objective.&quot;&lt;ref name=&quot;Hartmann&quot;&gt;{{cite journal
|author=J. Hartmann
|title=An Improvement of the Foucault Knife-Edge Test in the Investigation of Telescope Objectives
|journal=The Astrophysical Journal
|date=May 1908
|volume=27
|issue=
|pages=254-9
|url=http://adsabs.harvard.edu/abs/1908ApJ....27..254H
|arxiv=
|bibcode=1908ApJ....27..254H
|doi=10.1086/141552
|pmid=
|accessdate=2013-09-13 }}&lt;/ref&gt;

&quot;The star brightness increase in 1964 was considerably different in yellow and blue rays. ... Extensive tables and graphs represent the mean photographic and photovisual curve of V1329 Cyg observed in Moscow and Odessa, brightness curves in blue and yellow rays, brightness increases, and brightness minima before and after an outburst.&quot;&lt;ref name=&quot;Arkhipova&quot;&gt;{{cite journal
|author=V. P. Arkhipova; O. E. Mandel
|title=Photographic observations of V1329 CYG
|journal=Pis'ma v Astronomicheskii Zhurnal
|date=April 1991
|volume=17
|issue=04
|pages=359-67
|url=http://adsabs.harvard.edu/abs/1991PAZh...17..359A
|arxiv=
|bibcode=1991PAZh...17..359A
|doi=
|pmid=
|accessdate=2013-09-13 }}&lt;/ref&gt;

&quot;The GE Reveal bulb is marketed as the bulb that is made to “specially filter out yellow rays that hide life's true colors.” This is accomplished by the use of neodymium in the glass.&quot;&lt;ref name=&quot;Birriel&quot;&gt;{{cite journal
|author=Jennifer J. Birriel
|title=Demonstrating Absorption Spectra Using Commercially Available Incandescent Light Bulbs
|journal=Astronomy Education Review
|date=September 2008
|volume=7
|issue=2
|pages=147-57
|url=http://link.aip.org/link/?AERSCZ/7/147/1
|arxiv=
|bibcode=
|doi=10.3847/AER2008035
|pmid=
|accessdate=2013-09-13 }}&lt;/ref&gt;
{{clear}}

==Planetary sciences==
{{main|Planetary sciences}}
[[Image:Fajada Butte by RO.JPG|thumb|right|250px|Fajada Butte is in Chaco Canyon, New Mexico. Credit: [[c:user:Rationalobserver|Rationalobserver]].{{tlx|free media}}]]
&quot;U-Pb ages of zircon from the Firehole and Analcite ash beds in the Eocene Green River Formation (Wyoming, United States) are indistinguishable from &lt;sup&gt;40&lt;/sup&gt;Ar/&lt;sup&gt;39&lt;/sup&gt;Ar ages of sanidine after adjusting the latter to the astronomically calibrated age of 28.201 Ma for the Fish Canyon sanidine standard.&quot;&lt;ref name=&quot;MESmith&quot;/&gt;

&quot;Calibrating Green River Formation &lt;sup&gt;40&lt;/sup&gt;Ar/&lt;sup&gt;39&lt;/sup&gt;Ar ages to the 28.201 Ma age for Fish Canyon sanidine permits the first direct comparison of specific Green River Formation strata to the astronomical solution for Early Eocene insolation. This comparison supports the hypothesis that periods of fluvial deposition coincided with minima in long and short eccentricity, and that periods of lake expansion and evaporite deposition correspond to eccentricity maxima.&quot;&lt;ref name=&quot;MESmith&quot;/&gt;

&quot;Euhedral, pale yellow zircons were isolated from the Analcite and Firehole ash beds by hand-crushing and heavy liquid concentration.&quot;&lt;ref name=&quot;MESmith&quot;&gt;{{cite journal
|author=M. Elliot Smith, K.R. Chamberlain, B.S. Singer and A.R. Carroll
|title=Eocene clocks agree: Coeval &lt;sup&gt;40&lt;/sup&gt;Ar/&lt;sup&gt;39&lt;/sup&gt;Ar, U-Pb, and astronomical ages from the Green River Formation
|journal=Geology
|date= 2010
|volume=38
|issue=6
|pages=527-30
|url=http://geology.gsapubs.org/content/38/6/527.short
|arxiv=
|bibcode=
|doi=10.1130/G30630.1
|pmid=
|accessdate=2013-09-14 }}&lt;/ref&gt;
{{clear}}

==Color astronomy==
{{main|Radiation astronomy/Colors}}
[[Image:Color icon yellow.svg|thumb|right|250px|These are examples of the various colors of yellow. Credit: [[c:User:Badseed|Badseed]].{{tlx|free media}}]]
[[Image:PlanckianLocusWithYellowComplements.png|thumb|left|250px|Complements of yellow have a dominant wavelength in the range 380 to 480&amp;nbsp;nm. The green lines show several possible pairs of complementary colors. Credit: [[w:User:Dicklyon|Dicklyon]].{{tlx|free media}}]]
[[Image:Lascaux2.jpg|thumb|right|250px|The image is of a horse colored with [[w:yellow ochre|yellow ochre]]. from [[w:Lascaux|Lascaux]] cave. Credit: Cro-Magnon peoples.{{tlx|free media}}]]
[[Image:Zwei Bäume im Rapsfeld, blauer Himmel.jpg|thumb|left|250px|This shows a field of yellow rapeseed. Credit: [http://www.publicdomainpictures.net/browse-author.php?a=1 Petr Kratochvil].{{tlx|free media}}]]
'''Def.''' &quot;[t]he colour of [[wikt:gold|gold]] or [[wikt:butter|butter]]; the [[wikt:colour|colour]] obtained by mixing [[wikt:green|green]] and [[wikt:red|red]] light, or by subtracting [[wikt:blue|blue]] from [[wikt:white|white]] light&quot;&lt;ref name=&quot;YellowWikt&quot;&gt;{{cite journal
|title=yellow
|journal=Wiktionary
|publisher=Wikimedia Foundation, Inc
|location=San Francisco, California
|date=September 1, 2013
|url=https://en.wiktionary.org/wiki/yellow
|accessdate=2013-09-02 }}&lt;/ref&gt; is called '''yellow'''.

'''Def.'''

a bright yellow colour, resembling the metal gold

is called
{| class=&quot;wikitable&quot; style=&quot;text-align:center; margin:0.5em auto; width:auto; margin-left:1em;&quot;
|-
| style=&quot;background:#FFD700;&quot;|'''gold'''.
|}

Yellow, in the form of [[w:yellow ochre|yellow ochre]] pigment made from clay, was one of the first colors used in prehistoric cave art. The cave of [[w:Lascaux|Lascaux]] has an image of a horse colored with yellow estimated to be 17,300 years old.

[[w:Shades of yellow|Shades of yellow]] contains a more diverse set of yellow or yellow-like colors.
{{clear}}

==Minerals==
{{main|Radiation astronomy/Minerals}}
[[Image:Citrin cut.jpg|thumb|right|250px|Citrine is a deep golden yellowish variety of quartz. Credit: [[:de:user:Wela49|Wela49]].{{tlx|free media}}]]
Tarapacaite is a natural mineral pigment composed of potassium chromate which is a likely source of yellow.
{{clear}}

==Precious metal minerals==
{{main|Minerals/Metals/Precious}}
[[Image:GoldNuggetUSGOV.jpg|thumb|right|250px|This is an image of a naturally occurring gold nugget. Credit: USGS.{{tlx|free media}}]]
At right is an image of a piece of native gold discovered as part of a placer deposit, a gold nugget.
{{clear}}

==Chalcogen minerals==
{{main|Minerals/Chalcogens}}
[[Image:Soufresicile3.jpg|thumb|left|250px|The image shows native sulfur, yellow, and calcite crystals, clear or white. Credit: [[c:User:Archaeodontosaurus|Didier Descouens]].{{tlx|free media}}]]
[[Image:Sulfur.jpg|thumb|right|250px|This shows sulfur crystals from the Smithsonian Institution. Credit: [[w:User:Deglr6328|Deglr6328]].{{tlx|free media}}]]
Sulfur occurs [[w:nature|naturally]] as the pure [[w:element|element]] (native sulfur) and as [[w:Sulfide minerals|sulfide]] and [[w:sulfate minerals|sulfate minerals]]. Being abundant in native form, sulfur was known in ancient times, mentioned for its uses in [[w:ancient India|ancient India]], [[w:ancient Greece|ancient Greece]], [[w:History of China#Ancient China|China]] and [[w:ancient Egypt|Egypt]]. Octasulfur is a soft, bright-yellow solid with only a faint odor, similar to that of [[w:match|match]]es.
{{clear}}

==Cubanite==
[[Image:Cubanite-47299.jpg|thumb|right|250px|These are bronze to brass-yellow, striated, cyclically-twinned cubanite crystals from the Chibougamau mines of Quebec. Credit: [[c:User:Rob Lavinsky|Rob Lavinsky]].{{tlx|free media}}]]
'''Cubanite''' is a yellow mineral of copper, iron, and sulfur, CuFe&lt;sub&gt;2&lt;/sub&gt;S&lt;sub&gt;3&lt;/sub&gt;.&lt;ref name=&quot;Webmineral&quot;&gt;[http://www.webmineral.com/data/Cubanite.shtml Webmineral]&lt;/ref&gt; Cubanite occurs in high temperature [[w:hydrothermal|hydrothermal]] deposits with [[w:pyrrhotite|pyrrhotite]] and [[w:pentlandite|pentlandite]] as intergrowths with [[w:chalcopyrite|chalcopyrite]]. It results from [[w:exsolution|exsolution]] from chalcopyrite at temperatures below 200 to 210 °C.&lt;ref name=&quot;HBM&quot;&gt;[http://rruff.geo.arizona.edu/doclib/hom/cubanite.pdf Handbook of Mineralogy]&lt;/ref&gt; It has also been reported from [[w:carbonaceous chondrite|carbonaceous chondrite]] [[meteorites]].&lt;ref name=&quot;HBM&quot;/&gt;
{{clear}}

==Microlite==
[[Image:Microlite-Lepidolite-21663.jpg|thumb|right|250px|The image shows pale-yellow microlite on lepidolite. Credit: [[c:User:Rob Lavinsky|Rob Lavinsky]].{{tlx|free media}}]]
'''Microlite''' is composed of sodium calcium tantalum oxide with a small amount of fluorine (Na,Ca)&lt;sub&gt;2&lt;/sub&gt;Ta&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;6&lt;/sub&gt;(O,OH,F). Microlite is a mineral in the [[w:pyrochlore|pyrochlore]] group that occurs in [[w:pegmatite|pegmatite]]s and constitutes an [[w:ore|ore]] of tantalum. It has a [[w:Mohs hardness|Mohs hardness]] of 5.5 and a variable [[w:specific gravity|specific gravity]] of 4.2 to 6.4. It occurs as disseminated microscopic subtranslucent to opaque octahedral [[w:crystal|crystal]]s with a [[w:refractive index|refractive index]] of 2.0 to 2.2. Microlite is also called djalmaite. Microlite occurs as a primary mineral in lithium-bearing granite pegmatites, and in miarolitic cavities in granites.
{{clear}}

==Orpiment==
[[Image:Orpiment mineral.jpg|thumb|right|250px|Orpiment is a yellow to orange mineral on Earth. Credit: USGS.{{tlx|free media}}]]
'''Orpiment''', [Arsenic trisulfide] As&lt;sub&gt;2&lt;/sub&gt;S&lt;sub&gt;3&lt;/sub&gt;, is a common monoclinic arsenic sulfide mineral. Orpiment is an orange to yellow mineral that is found worldwide [on Earth], and occurs as a sublimation product in volcanic fumaroles, low temperature hydrothermal veins, hot springs and as a byproduct of the decay of another arsenic mineral, realgar.
{{clear}}

==Pyrite==
[[Image:2780M-pyrite1.jpg|thumb|right|250px|Pyrite cubic crystals are on marl from Navajún, Rioja, Spain. Credit: [[c:User:CarlesMillan|CarlesMillan]].{{tlx|free media}}]]
The mineral '''pyrite''', or '''iron pyrite''', is an iron sulfide with the [[w:chemical formula|formula]] [[w:iron|Fe]][[w:sulfur|S]]&lt;sub&gt;2&lt;/sub&gt;. This mineral's metallic [[w:Luster (mineralogy)|luster]] and pale brass-yellow hue have earned it the nickname '''fool's gold''' because of its superficial resemblance to gold. Pyrite is the most common of the [[w:sulfide mineral|sulfide mineral]]s [on Earth]. Pyrite is usually found associated with other sulfides or oxides in quartz [[w:Vein (geology)|veins]], [[w:sedimentary rock|sedimentary rock]], and [[w:metamorphic rock|metamorphic rock]], as well as in [[w:coal|coal]] beds, and as a replacement mineral in [[w:fossil|fossil]]s. Despite being nicknamed fool's gold, pyrite is sometimes found in association with small quantities of gold. Gold and arsenic occur as a coupled substitution in the pyrite structure. In the [[w:Carlin–type gold deposit|Carlin–type gold deposit]]s, arsenian pyrite contains up to 0.37 wt% gold.&lt;ref name=&quot;Fleet&quot;&gt;M. E. Fleet and A. Hamid Mumin, [http://www.minsocam.org/msa/AmMin/toc/Articles_Free/1997/Fleet_p182-193_97.pdf Gold-bearing arsenian pyrite and marcasite and arsenopyrite from Carlin Trend gold deposits and laboratory synthesis], American Mineralogist 82 (1997) pp. 182–193&lt;/ref&gt;
{{clear}}

==Satterlyite==
[[Image:Satterlyite - Rapid Creek.jpg|thumb|right|250px|This Satterlyite sample is from the Rapid Creek area of northern [[w:Yukon|Yukon]], Canada. Credit: [[c:User:Chris857|Chris857]].{{tlx|free media}}]]
'''Satterlyite''' is a [[w:hydroxyl|hydroxyl]] bearing iron [[w:phosphate mineral|phosphate mineral]]. The mineral can be found in phosphetic [[w:shale|shale]]s. Satterlyite is part of the phosphate mineral group. Satterlyite is a transparent, light brown to light yellow mineral. Satterlyite has a formula of (Fe&lt;sup&gt;2+&lt;/sup&gt;,Mg,Fe&lt;sup&gt;3+&lt;/sup&gt;)&lt;sub&gt;2&lt;/sub&gt;(PO&lt;sub&gt;4&lt;/sub&gt;)(OH). Satterlyite occurs in nodules in shale in the Big Fish River (Mandarino, 1978). These nodules were about 10 cm in diameter, some would consist of satterlyite only and others would show satterlyite with quartz, pyrite, wolfeite or maricite.

&quot;[[w:Holtedahlite|Holtedahlite]], a mineral that was found in Tingelstadtjern quarry in Norway, with the formula (Mg&lt;sub&gt;12&lt;/sub&gt;PO&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;5&lt;/sub&gt;(PO&lt;sub&gt;3&lt;/sub&gt;OH,CO&lt;sub&gt;3&lt;/sub&gt;)(OH,O)&lt;sub&gt;6&lt;/sub&gt; is isostructural with satterlyite (Raade, 1979). [[w:Infrared absorption|Infrared absorption]] powder spectra show that satterlyite is different than natural haltedahlite in that there is no carbonate for phosphate substitution (Kolitsch, 2002). Satterlyite is also structurally related to [[w:phosphoellenbergerite|phosphoellenbergerite]], a mineral that was discovered in Modum, Norway; near San Giocomo Vallone Di Gilba, in Western Alps of Italy (Palache, 1951); the minerals formula is Mg&lt;sub&gt;14&lt;/sub&gt;(PO&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;5&lt;/sub&gt;(PO&lt;sub&gt;3&lt;/sub&gt;OH)&lt;sub&gt;2&lt;/sub&gt;(OH)&lt;sub&gt;6&lt;/sub&gt; (Kolitsch, 2002).
{{clear}}

==Actinide minerals==
{{main|Minerals/Actinides}}
[[Image:Carnotite-BYU.jpg|thumb|right|250px|The Carnotite is from the Happy Jack Mine, Utah. Credit: USGS.{{tlx|free media}}]]
'''Carnotite''' is a potassium uranium [[w:vanadate|vanadate]] [[w:radioactive|radioactive]] mineral with [[w:chemical formula|chemical formula]]: [[w:potassium|K]]&lt;sub&gt;2&lt;/sub&gt;([[w:uranium|U]][[w:oxygen|O]]&lt;sub&gt;2&lt;/sub&gt;)&lt;sub&gt;2&lt;/sub&gt;([[w:vanadium|V]]O&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;2&lt;/sub&gt;'''·'''3H&lt;sub&gt;2&lt;/sub&gt;O. The water content can vary and small amounts of calcium, barium, magnesium, iron, and sodium are often present. ... Carnotite is a bright to greenish yellow mineral that occurs typically as crusts and flakes in sandstones. Amounts as low as one percent will color the sandstone a bright yellow. The high uranium content makes carnotite an important uranium ore and also radioactive. It is a secondary vanadium and uranium mineral usually found in [[w:sedimentary rocks|sedimentary rocks]] in arid climates. It is an important ore of uranium in the [[w:Colorado Plateau|Colorado Plateau]] region of the [[w:United States|United States]] where it occurs as disseminations in [[w:sandstone|sandstone]] and concentrations around [[w:petrified|petrified]] logs.
{{clear}}

==Silicate minerals==
{{main|Geominerals/Silicates}}
[[Image:Spurrite Calcium silicate and carbonate Luna county New mexico 1873.jpg|thumb|right|250px|This image shows yellow-brown spurrite from New Mexico, USA. Credit: Dave Dyet.{{tlx|free media}}]]
'''Spurrite''' is a [[w:Nesosilicate|nesosilicate]] that can occur naturally as a yellow mineral. &quot;Its [[w:chemical formula|chemical formula]] is [[w:calcium|Ca]]&lt;sub&gt;5&lt;/sub&gt;([[w:silicon|Si]][[w:oxygen|O]]&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;2&lt;/sub&gt;[[w:carbon|C]]O&lt;sub&gt;3&lt;/sub&gt;.&lt;ref name=&quot;Gaines&quot;&gt;Richard V. Gaines, H. Catherine W. Skinner, Eugene E. Foord, Brian Mason, and Abraham Rosenzweig: ''Dana's new mineralogy'', p. 1106. John Wiley &amp; Sons, 1997&lt;/ref&gt; Spurrite is generally formed in [[w:contact metamorphism|contact metamorphism]] zones as [[w:mafic|mafic magma]]s are intruded into [[w:carbonate rock|carbonate rock]]s.&lt;ref name=&quot;Smith&quot;&gt;Smith, J.V. (1960) &quot;The Crystal structure of Spurrite, Ca&lt;sub&gt;5&lt;/sub&gt;(SiO&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;2&lt;/sub&gt;CO&lt;sub&gt;3&lt;/sub&gt;&quot;. ''Acta. Cryst.'' 13, 454&lt;/ref&gt;
{{clear}}

==Mineraloids==
{{main|Chemicals/Mineraloids}}
[[Image:LimoniteUSGOV.jpg|thumb|right|250px|Limonite is an amorphous mineraloid of a range of hydrated iron oxides. Credit: USGS.{{tlx|free media}}]]
'''Limonite''' is an [[w:iron ore|iron ore]] consisting of a mixture of hydrated [[w:iron(III) oxide-hydroxide|iron(III) oxide-hydroxide]]s in varying composition. The generic formula is frequently written as FeO(OH)·nH&lt;sub&gt;2&lt;/sub&gt;O, although this is not entirely accurate as the ratio of oxide to hydroxide can vary quite widely. Limonite is one of the two principle iron ores, the other being [[w:hematite|hematite]], and has been [[w:mining|mined]] for the production of iron since at least 2500 BCE.&lt;ref name=&quot;MacEachern&quot;&gt;MacEachern, Scott (1996) [http://www.panafprehistory.org/images/papers/IRON_AGE_BEGINNINGS_NORTH_OF_THE_MANDARA_MOUNTAINS_CAMEROON_AND_NIGERIA_Scott_MacEachern.pdf &quot;Iron Age beginnings north of the Mandara Mountains, Cameroon and Nigeria&quot;] pp. 489&amp;ndash;496 ''In'' Pwiti, Gilbert and Soper, Robert (editors) (1996) ''Aspects of African Archaeology: Proceedings of the Tenth Pan-African Congress'' University of Zimbabwe Press, Harare, Zimbabwe, {{ISBN|978-0-908307-55-5}}; archived [http://liveweb.archive.org/http://www.panafprehistory.org/images/papers/IRON_AGE_BEGINNINGS_NORTH_OF_THE_MANDARA_MOUNTAINS_CAMEROON_AND_NIGERIA_Scott_MacEachern.pdf here] by Internet Archive on 11 March 2012&lt;/ref&gt;&lt;ref name=&quot;Maes&quot;&gt;Diop-Maes, Louise Marie (1996) [http://www.ankhonline.com/revue/diop_lm_metallurgie_fer_afrique.htm &quot;La question de l'Âge du fer en Afrique&quot; (&quot;The question of the Iron Age in Africa&quot;)] ''Ankh'' 4/5: pp. 278&amp;ndash;303, in French; archived [http://web.archive.org/web/20080125103929/http://www.ankhonline.com/revue/diop_lm_metallurgie_fer_afrique.htm here] by Internet Archive on 25 January 2008&lt;/ref&gt; Although originally defined as a single mineral, limonite is now recognized as a mixture of related hydrated [[w:iron oxide|iron oxide]] minerals, among them [[w:goethite|goethite]], [[w:akaganeite|akaganeite]], [[w:lepidocrocite|lepidocrocite]], and [[w:jarosite|jarosite]]. Individual minerals in limonite may form crystals, but limonite does not, although specimens may show a fibrous or microcrystalline structure,&lt;ref name=&quot;Boswell&quot;&gt;Boswell, P. F. and Blanchard, Roland (1929) &quot;Cellular structure in limonite&quot; ''Economic Geology'' 24(8):&amp;nbsp;pp.&amp;nbsp;791&amp;ndash;796&lt;/ref&gt; and limonite often occurs in concretionary forms or in compact and earthy masses; sometimes mammillary, [[w:botryoidal|botryoidal]], reniform or stalactitic. Because of its amorphous nature, and occurrence in hydrated areas limonite often presents as a clay or mudstone. However there are limonite [[w:pseudomorph|pseudomorph]]s after other minerals such as pyrite.&lt;ref name=&quot;Northrop&quot;&gt;Northrop, Stuart A. (1959) &quot;Limonite&quot; ''Minerals of New Mexico'' (revised edition) University of New Mexico Press, Albuquerque, New Mexico, pp. 329&amp;ndash;333 }}&lt;/ref&gt; This means that chemical weathering transforms the crystals of pyrite into limonite by hydrating the molecules, but the external shape of the pyrite crystal remains. Limonite pseudomorphs have also been formed from other iron oxides, hematite and magnetite; from the carbonate [[w:siderite|siderite]] and from iron rich silicates such as [[w:Almandine|almandine garnets]]. Limonite usually forms from the hydration of hematite and magnetite, from the oxidation and hydration of iron rich sulfide minerals, and chemical weathering of other iron rich minerals such as olivine, pyroxene, amphibole, and biotite. It is often the major iron component in [[w:Laterite|lateritic soils]]. One of the first uses was as a [[w:pigment|pigment]]. The yellow form produced yellow [[w:ochre|ochre]] for which [[w:Cyprus|Cyprus]] was famous.&lt;ref name=&quot;Constantinou&quot;&gt;Constantinou, G. and Govett, G. J. S. (1972) &quot;Genesis of sulphide deposits, ochre and umber of Cyprus&quot; ''Transactions of the Institution of Mining and Metallurgy'' 81:&amp;nbsp;pp.&amp;nbsp;34&amp;ndash;46&lt;/ref&gt;

==Theoretical yellow astronomy==
[[Image:Yellow sprites lg.jpg|thumb|right|250px|Sprites are imaged above Kansas on 10 August 2000. Credit: [[c:user:Bob Jackson~commonswiki|Bob Jackson~commonswiki]].{{tlx|free media}}]]
Here's a [[Definitions/Theory#Theoretical definition|theoretical definition]]:

'''Def.''' astronomy applied to the various terrestrial or extraterrestrial yellow sources of radiation, especially at night is called '''yellow astronomy'''.

It is also conducted above the Earth's atmosphere and at locations away from the Earth as a part of explorational (or exploratory) yellow astronomy.

&quot;The lack of long period Cepheids of Population I with ''P'' &gt; 45 d in the Galaxy as opposed to the Magellanic Clouds, has fascinated observers and theoreticians for many years.&quot;&lt;ref name=&quot;Genderen&quot;&gt;{{cite journal
|author=A. M. van Genderen
|title=A Discussion on Three Yellow Variable Supergiants in and Near the Cepheid Instability Strip: V 810 Cen (=HD 101947), Tr. 27-102 (=HD 159378) and BL Tel (F), Based on ''VBLUW'' Photometry and the Long-period Cepheids Absence in the Galaxy
|journal=Astronomy &amp; Astrophysics
|date=August 1980
|volume=88
|issue=1-2
|pages=77-83
|url=http://adsabs.harvard.edu/abs/1980A%26A....88...77V
|arxiv=
|bibcode=1980A%26A....88...77V
|doi=
|pmid=
|accessdate=2013-09-16 }}&lt;/ref&gt;
{{clear}}

==Entities==
{{main|Radiation astronomy/Entities}}
[[Image:Sri Mariamman Temple Singapore 2 amk.jpg|thumb|left|250px|A Statue of Krishna in the Sri Mariamman Temple, Singapore has Krishna shown with a flute. Credit: [[c:User:AngMoKio|AngMoKio]].{{tlx|free media}}]]
[[Image:Krishna halo white cow peacock.jpg|thumb|right|250px|The image shows the classical planet Krishna leaning against a white cow. Credit: Parvati and Ossopunk.{{tlx|fairuse}}]]
'''Krishna''' is the Daśāvatāra eighth avatar incarnation of Lord Vishnu in Hinduism. Worship of the deity Krishna, either in the form of Vasudeva, Bala Krishna or Gopala can be traced to as early as 4th century BC.&lt;ref name=&quot;Cultofgopal&quot;&gt;{{cite book
|title = A Revolution in Kṛṣṇaism: The Cult of Gopāla: History of Religions, Vol. 25, No. 4 (May, 1986 ), pp. 296-317
|publisher = www.jstor.org
|last = Hein
|first = Norvin
|jstor = 1062622
|url=http://www.jstor.org/stable/1062622
}}&lt;/ref&gt;&lt;ref name = &quot;Hastings540&quot;&gt;{{cite book
|author =James Rodney Hastings and John A Selbie
|title = Encyclopedia of Religion and Ethics
|edition = 2nd edition 1925-1940, reprint 1955, 2003
|language =
|publisher = Kessinger Publishing, LLC
|location = Edinburgh
|year = 1908
|page = 476
|isbn = 0-7661-3673-6
|oclc =
|doi =
|url = http://books.google.com/?id=Kaz58z--NtUC&amp;pg=PA540&amp;vq=Krishna
|accessdate = 2008-05-03 }}pp.540-42&lt;/ref&gt; He is often shown wearing a yellow silk [[w:dhoti|dhoti]] and a peacock feather crown. The [[w:Harivamsa|Harivamsa]] describes intricate relationships between Krishna Vasudeva, Sankarsana, Pradyumna and Aniruddha that would later form a [[w:Vaishnava|Vaishnava]] concept of primary quadrupled expansion, or [[w:avatar|avatar]].&lt;ref name=&quot;Couture&quot;&gt;{{cite journal
|title= The emergence of a group of four characters (Vasudeva, Samkarsana, Pradyumna, and Aniruddha) in the Harivamsa: points for consideration
|journal = Journal of Indian Philosophy
|author = Couture, André
|authorlink=
|coauthors=
|year= 2006
|publisher=
|location=
|volume = 34
|issue = 6
|pages= 571–585
|url=http://www.springerlink.com/index/141N2426N4806068.pdf
|doi= 10.1007/s10781-006-9009-x
|ref= harv
}}&lt;/ref&gt;

&quot;The Hindu ''Atharva Veda'' speaks of the &quot;four heavenly directions, having the wind as lord, upon which the sun looks out.&quot;&lt;sup&gt;63&lt;/sup&gt; This, of course, can only be the central sun, who is Brahma, a god of ''four faces''. The myths also attribute four faces to Shiva.&lt;sup&gt;64&lt;/sup&gt; The central sun Prajapati takes the form of the four-eyed, four-faced, and four-armed Vivvakarman, the &quot;all maker&quot;.&lt;sup&gt;65&lt;/sup&gt; Agni, too, faces &quot;in all directions,&quot;&lt;sup&gt;66&lt;/sup&gt; as does Krishna.&lt;sup&gt;67&lt;/sup&gt; ... There can no longer be any doubt that the four-eyed or four-faced god is Saturn, for the sun-planet appears in Babylonian myth as Ea (Sumerian Enki)-a god of ''four eyes'' that &quot;behold all things.&quot;&lt;sup&gt;73&lt;/sup&gt;&quot;&lt;ref name=&quot;Talbott&quot;&gt;{{cite book
|author=David N. Talbott
|title=The Saturn Myth
|publisher=Knopf Doubleday &amp; Company, Inc.
|location=Garden City, New York, USA
|date=1980
|editor=
|pages=419
|url=http://books.google.com/books?id=tNVlQgAACAAJ&amp;hl=en
|arxiv=
|bibcode=
|doi=
|pmid=
|isbn=0-385-11376-5
|accessdate=2013-01-03 }}&lt;/ref&gt;

&quot;The bansuri is one of the most important instruments in Hindu mythology. It was the instrument played by Krishna, who Hindus believe is the eighth reincarnation of the god Vishnu, when he was in child form. Its use in Buddhist paintings can be identified as early as CE 100.&quot;&lt;ref name=&quot;Bloke&quot;&gt;{{cite book
|author=that bloke on the underground
|title=Bansuri
|publisher=Indian Music Project
|location=
|date=8 October 2013
|url=http://indianmusicproject.blogspot.com/
|accessdate=2015-12-02 }}&lt;/ref&gt;
{{clear}}

==Radiation astronomy sources==
{{main|Radiation astronomy/Sources}}
[[Image:MountRedoubtEruption.jpg|thumb|right|250px|Mount Redoubt in Alaska erupted on April 21, 1990. The mushroom-shaped plume rose from avalanches of hot debris that cascaded down the north flank. Credit: R. Clucas, USGS.{{tlx|free media}}]]
'''Notation:''' let the symbol EMSS represent the '''''Einstein Medium Sensitivity Survey'''''.

The &quot;presence of an excess of X-ray luminous &quot;yellow&quot; stars, already found with the analysis of the stellar content of the ''Einstein'' Medium Sensitivity Survey (MSS), is confirmed by the EMSS, whose substantially larger size sample allows to draw conclusions with a higher statistical significance than the MSS&quot;&lt;ref name=&quot;Sciortino&quot;&gt;{{cite journal
|author=S. Sciortino, F. Favata, and G. Micela
|title=The stellar coronal component of the Galaxy. II. an analysis of the stellar content of the ''Einstein'' Extended Medium Sensitivity Survey
|journal=Astronomy and Astrophysics
|date=April 1995
|volume=296
|issue=04
|pages=370-9
|url=http://adsabs.harvard.edu/full/1995A%26A...296..370S
|arxiv=
|bibcode=1995A&amp;A...296..370S
|doi=
|pmid=
|accessdate=2013-09-16 }}&lt;/ref&gt;.

An &quot;excess of X-ray luminous &quot;yellow&quot; stars in the X-ray selected samples, [have been] tentatively identified with a population of active RS CVn-like binaries, or a population of active young late-type stars.&quot;&lt;ref name=&quot;Sciortino&quot;/&gt;

&quot;The comparison between ... model predictions and the observed stellar source counts for yellow stars in the reference EMSS subsample shows a clear excess that peaks in the F-G spectral type range where the 70 observed sources have to be compared with the ~24 predicted ones. This excess is statistically significant at more than 99.8% level. ... this excess is concentrated for ''B'' - ''V'' ranging from 0.5 to 1.0 (corresponding to ''m''&lt;sub&gt;v&lt;/sub&gt; ranging from 8 to 12) which corresponds, in the EMSS, to normal main sequence stars with spectral type comprised between F and early K.&quot;&lt;ref name=&quot;Sciortino&quot;/&gt;

This &quot;excess is real, and most likely doe to some high X-ray luminosity population with optical characteristics similar to normal main sequence yellow stars.&quot;&lt;ref name=&quot;Sciortino&quot;/&gt;

There is also &quot;an excess for the A/F star groups mainly due to the occurrence of stars with f&lt;sub&gt;x&lt;/sub&gt;/f&lt;sub&gt;v&lt;/sub&gt; ratio higher than the mean values for each group and suggest that this could be explained by the occurrence of a large number of X-ray unresolved binary systems with an active M star companion than the predicted ones.&quot;&lt;ref name=&quot;Sciortino&quot;/&gt;

&quot;For yellow stars, the current state-of-art knowledge in terms of X-ray luminosity functions is not able to account for all of the observed yellow stellar sources in the EMSS, so that, to explain the observed source counts, a new population of stellar-like X-ray emitting sources with optical characteristics similar to normal main sequence yellow stars must be hypothesized. ... based on current knowledge, this population is likely to be (at least partly) composed of very young (and therefore highly X-ray luminous) yellow stars, perhaps of the kind variously indicated by previous authors as WTTS or NTTS, or simply by near ZAMS objects.&quot;&lt;ref name=&quot;Sciortino&quot;/&gt;
{{clear}}

==Objects==
{{main|Radiation astronomy/Objects|Object astronomy}}
[[Image:XZ Tauri - HL Tauri.png|thumb|right|250px|The NASA/ESA Hubble Space Telescope has snapped a striking view of a multiple star system called XZ Tauri, its neighbour HL Tauri and several nearby young stellar objects. Credit: ESA/Hubble &amp; NASA, Acknowledgement: Judy Schmidt.{{tlx|free media}}]]
XZ Tauri is blowing a hot bubble of gas into the surrounding space, which is filled with bright and beautiful clumps that are emitting strong winds and jets. These objects illuminate the region.

&quot;An abundance analysis of the yellow symbiotic system AG Draconis reveals it to be a metal-poor K-giant ([Fe/H]=-1.3) which is enriched in the heavy s-process elements. ... the other yellow symbiotic stars are probably low-metallicity objects as well.&quot;&lt;ref name=&quot;VVSmith&quot;/&gt;
{{clear}}

==Continua==
{{main|Radiation astronomy/Continua}}
[[Image:20140314 RJ.JPG|thumb|right|250px|Yellow continua is exhibited during a sunset in Rio de Janeiro. Credit: [[c:user:Rosimeria|Rosimeria]].{{tlx|free media}}]]
In Fig. 4, &quot;A density tracing of the spectrum of ''θ'' Lyr, K0 II. Straight chords through the yellow continuum toward the blue and from λ 4750 along the green depression to the Mg I &quot;b&quot; triplet lines define the break-angle α (α here is about 12°).&quot;&lt;ref name=&quot;Spinrad&quot;&gt;{{cite journal
|author=Hyron Spinrad and David B. Wood
|title=Magnesium Hydride in Cool Stars and Galaxies
|journal=The Astrophysical Journal
|date=January 1965
|volume=141
|issue=01
|pages=109-14
|url=http://adsabs.harvard.edu/abs/1965ApJ...141..109S
|arxiv=
|bibcode=1965ApJ...141..109S
|doi=10.1086/148092
|pmid=
|accessdate=2013-09-18 }}&lt;/ref&gt;
{{clear}}

==Emissions==
{{main|Radiation astronomy/Emissions}}
[[Image:NGC 6302 with (Fe II) Emission.png|thumb|right|250px|Observations reveal [Fe II] emission, shown here in pink, along the edges of the biopolar outflows of this young planetary nebula. Credit: [https://www.flickr.com/people/54209675@N00 Judy Schmidt from USA].{{tlx|free media}}]]
Red screen: F164N ([Fe II]) Red: F673N Yellow-Green: F658N Blue: F373N. North is 35.20° clockwise from up.

Emission lines are usually unique to the chemical elements. As the emissions are produced by the release of specific wavelength photons when electrons drop to a lower energy level, absorption lines may be produced as electrons rise to this higher energy level.
{{clear}}

==Bands==
{{main|Radiation astronomy/Bands}}
[[Image:Band of yellow.jpg|thumb|right|250px|Sunset is in Wiltshire. Credit: Stewart Black.{{tlx|free media}}]]
&quot;Data in two spectral bands (green: λ 5253-5353, and yellow: λ 5824-5844) were taken on several sunspot groups during February 1974. ... the general level of circular polarization is weaker [in the yellow band]. The peak magnitudes of the linear polarization [''P''&lt;sub&gt;''L''&lt;/sub&gt; ≡ (''Q''&lt;sup&gt;2&lt;/sup&gt; + ''U''&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;½&lt;/sup&gt;/''I''] (Figs. 1C and 2C) are comparable in both colors; the spatial distribution is, however, markedly different. Whereas in the green ''P''&lt;sub&gt;''L''&lt;/sub&gt; is fairly uniform over both type 1 [penumbra] and 2 [&quot;speckled&quot; possibly umbra] regions, in the yellow ''P''&lt;sub&gt;''L''&lt;/sub&gt; appears strong only in region 2; the linear polarization associated with region 1 has nearly vanished.&quot;&lt;ref name=&quot;Illing&quot;&gt;{{cite journal
|author=R. M. E. Illing, D. A. Landman, &amp; D. L. Mickey
|title=Broad-band circular polarization of sunspots - Spectral dependence and theory
|journal=Astronomy and Astrophysics
|date=June 1975
|volume=41
|issue=2
|pages=183-5
|url=http://adsabs.harvard.edu/full/1975A%26A....41..183I
|arxiv=
|bibcode=1975A&amp;A....41..183I
|doi=
|pmid=
|accessdate=2013-09-16 }}&lt;/ref&gt;

&quot;The behavior of the azimuth of the linear polarization at various points in the sunspot is markedly different in the two colors. In the green, one can clearly see a generally radial pattern over the entire spot; no such general pattern is apparent in the yellow, but a less pronounced radial pattern in the core of the spot does remain. It should be noted that the more complex area in the green corresponds to the &quot;speckled&quot; type 2 region.&quot;&lt;ref name=&quot;Illing&quot;/&gt;
{[clear}}

==Backgrounds==
{{main|Radiation astronomy/Backgrounds}}
[[Image:Yellow horizon.jpg|thumb|right|250px|It was a beautiful view from Narendra nagar on the way from Tehri garhwal about 5:00 pm. Credit: [[c:user:Naresh Sirola|Naresh Sirola]].{{tlx|free media}}]]
&quot;To greet the eyes of visitors as they first enter the Planetarium Building, there is planned a large decorative painting in oil, in three panels, illustrating American Indian astronomical mythology. Although primarily from the Blackfeet, the myths selected are those of rather wide distribution with little variation among the various tribes of North America. The left panel shows the Northern Lights or Aurora Borealis in the form of an arch in all the delicate colors, in which may be dimly seen the figures of the White Men of the North dancing around their camp-fires. The central panel shows the sun-god on a brilliant yellow background, the moon-goddess on a paler background, while in the upper right may be seen the Pleiades as conceived by the Indians, and in the upper left the Big Dipper and the North Star, these corner representations with the Milky Way or sky-trail between them are shown in silver on a background of deep blue.&quot;&lt;ref name=Fisher&gt;{{cite journal
|author=Clyde Fisher
|title=The Hayden Planetarium of the American Museum of Natural History
|journal=Popular Astronomy
|date=May 1934
|volume=42
|issue=415
|pages=233-43
|url=http://articles.adsabs.harvard.edu//full/1934PA.....42..233F
|arxiv=
|bibcode=1934PA.....42..233F
|doi=
|pmid=
|accessdate=2013-09-18 }}&lt;/ref&gt;

&quot;Placed between two Nicols, the [quartz] plate has the appearance [:] When the corresponding diagonals of the Nicols are parallel, or nearly so, the bands arc white upon a deep reddish-purple ground, [...]; with the Nicols crossed, the bands are dark upon a light greenish-yellow background, [...].&quot;&lt;ref name=Wright/&gt;

&quot;The quartz plate was placed in one end of a tube, large enough to admit its full size very nearly, and 11 inches in length. [...] In the other end was placed a good-sized Nicol; [...] Thus mounted the plate and Nicol form a polariscope of extraordinary sensibility, with faint light far excelling the best Savart, and even with strong light somewhat superior to it.&quot;&lt;ref name=Wright/&gt;

&quot;The instrument is especially suited for the determination of small degrees of polarization, and the examination of very faint lights.&quot;&lt;ref name=Wright/&gt;

Observations &quot;upon the zodiacal light [...] made to determine whether or not any portion of the light is polarized, [...] the amount of polarization necessary increases very greatly as the light becomes fainter, and especially so as it approaches the limit of visibility.&quot;&lt;ref name=Wright&gt;{{ cite book
|author=Arthur W. Wright
|title=on the Polarization of the Zodiacal Light, In: ''The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science''
|publisher=Taylor and Francis
|location=Red Lion Court, Fleet Street, London
|date=July-December 1874
|editor=Robert Kane, William Thomson and William Francis
|pages=13-21
|url=https://www.google.com/books/edition/The_London_Edinburgh_and_Dublin_Philosop/j-gXAAAAYAAJ?hl=en&amp;gbpv=1&amp;pg=PA16&amp;printsec=frontcover
|arxiv=
|bibcode=
|doi=
|pmid=
|isbn=
|accessdate=13 January 2022 }}&lt;/ref&gt;

&quot;On the completion of the instrument the first favourable opportunity was improved to test its efficiency upon the zodiacal light. It was almost immediately found to indicate the existence of light polarized in a plane passing through the sun. The bands were fainter than had been expected, and at first were overlooked. [...] On looking through the tube at the zodiacal, and turning the whole instrument slowly round, it was possible to find a position where the bands could be seen, and their nature and direction determined.&quot;&lt;ref name=Wright/&gt;

&quot;The results of the numerous observations of different evenings were entirely concordant, and showed that the plane of polarization passes through the sun, as nearly as it was possible to fix its direction.&quot;&lt;ref name=Wright/&gt;

&quot;The fact of polarization implies that the light is reflected, either wholly or in part, and is thus derived originally from the sun.&quot;&lt;ref name=Wright/&gt;

&quot;The results of the investigation may be summarized as follows:&quot;&lt;ref name=Wright/&gt;
# The zodiacal light is polarized in a plane passing through the sun.
# The amount of polarization is, with a high degree of probability, as much as 15 per cent., but can hardly be as much as 20 per cent.
# The spectrum of the light is not perceptibly different from that of sunlight, except in intensity.
# The light is derived from the sun, and is reflected from solid matter.
# This solid matter consists of small bodies (meteoroids) revolving about the sun in orbits crowded together toward the ecliptic.
{{clear}}

==Meteors==
{{main|Radiation/Meteors}}
[[Image:Looking Down on a Shooting Star.JPG|thumb|right|250px|This astronaut photograph was taken from the International Space Station while over China (approximately 400 kilometres to the north-west of Beijing), provides the unusual perspective of looking down on a meteor as it passes through the atmosphere. Credit: ISS Expedition 28 crew.{{tlx|free media}}]]
&quot;The train spectrum consisted of a red continuum, yellow continuum, and about 50 atomic lines between 3700–9000 Å. The yellow continuum, possibly due to NO&lt;sub&gt;2&lt;/sub&gt;, was also detected in the persistent train.&quot;&lt;ref name=&quot;Borovicka&quot;&gt;{{cite journal
|author=Jiří Borovička, Peter Jenniskens
|title=Time resolved spectroscopy of a Leonid fireball afterglow
|journal=Earth, Moon, and Planets
|date= 2000
|volume=82-83
|issue=
|pages=399-428
|url=http://link.springer.com/article/10.1023/A:1017071524899
|arxiv=
|bibcode=10.1023/A:1017071524899
|doi=
|pmid=
|accessdate=2013-09-18 }}&lt;/ref&gt;

&quot;On November 18, 1999 at 04&lt;sup&gt;h&lt;/sup&gt;00&lt;sup&gt;m&lt;/sup&gt;29&lt;sup&gt;s&lt;/sup&gt; UT, about two hours after the maximum of the 1999 Leonid meteor storm, a very bright Leonid meteor appeared over the island of Corse, France, and produced an afterglow evolving into a persistent train that was visible to the naked eye for several minutes.&quot;&lt;ref name=&quot;Borovicka&quot;/&gt;
{{clear}}

==Cosmic rays==
{{main|Radiation/Cosmic rays}}
[[Image:W44 supernova remnant.jpg|thumb|right|250px|The W44 supernova remnant is nestled within and interacting with the molecular cloud that formed its parent star. Credit: NASA/DOE/Fermi LAT Collaboration, NRAO/AUI, JPL-Caltech, ROSAT.{{tlx|free media}}]]
Fermi's LAT detects GeV gamma rays (magenta) produced when the gas is bombarded by cosmic rays, primarily protons. Radio observations (yellow) from the Karl G. Jansky Very Large Array near Socorro, N.M., and infrared (red) data from NASA's Spitzer Space Telescope reveal filamentary structures in the remnant's shell. Blue shows X-ray emission mapped by the Germany-led ROSAT mission.

&quot;The yellow supergiant content of nearby galaxies can provide a critical test of stellar evolution theory, bridging the gap between the hot, massive stars and the cool red supergiants. But, this region of the color-magnitude diagram is dominated by foreground contamination, requiring membership to somehow be determined.&quot;&lt;ref name=&quot;Drout&quot;/&gt;

&quot;The program exposures were extracted, using the dome flat field exposures as reference, and wavelength corrected. As the He-Ne-Ar exposures were obtained in the afternoon, and the grating might even be removed and reinserted before the program exposures, a zero-point shift in wavelength was determined for each of the M31 spectra using the O I λ5577 night sky line. ... Consecutive exposures of each M31 configuration were then summed, after '''cosmic rays''' were first identified and removed by comparing a median of the exposures to the individual exposures.&quot;&lt;ref name=&quot;Drout&quot;&gt;{{cite journal
|author=Maria R. Drout, Philip Massey, Georges Meynet, Susan Tokarz and Nelson Caldwell
|title=Yellow Supergiants in the Andromeda Galaxy (M31)
|journal=The Astrophysical Journal
|date=September 2009
|volume=703
|issue=1
|pages=441-60
|url=http://iopscience.iop.org/0004-637X/703/1/441/fulltext/
|arxiv=0907.5471
|bibcode=2009ApJ...703..441D
|doi=10.1088/0004-637X/703/1/441
|pmid=
|accessdate=2013-09-21 }}&lt;/ref&gt; Bold added.
{{clear}}

==Neutrons==
{{main|Radiation/Neutrons}}
[[Image:PIA03800 Global Map of Epithermal Neutrons.jpg|thumb|right|250px|Observations by NASA's 2001 Mars Odyssey spacecraft show a global view of Mars in intermediate-energy, or epithermal, neutrons. Credit: NASA/JPL/University of Arizona/Los Alamos National Laboratories.{{tlx|free media}}]]
Soil enriched by hydrogen is indicated by the deep blue colors on the map, which show a low intensity of epithermal neutrons. Progressively smaller amounts of hydrogen are shown in the colors light blue, green, yellow and red. The deep blue areas in the polar regions are believed to contain up to 50 percent water ice in the upper one meter (three feet) of the soil. Hydrogen in the far north is hidden at this time beneath a layer of carbon dioxide frost (dry ice). Light blue regions near the equator contain slightly enhanced near-surface hydrogen, which is most likely chemically or physically bound because water ice is not stable near the equator. The view shown here is a map of measurements made during the first three months of mapping using the neutron spectrometer instrument, part of the gamma ray spectrometer instrument suite. The central meridian in this projection is zero degrees longitude. Topographic features are superimposed on the map for geographic reference.

&quot;A comparison of the heavy-element abundance distribution in [AG Draconis] with theoretical nucleosynthesis calculations shows that the s-process is defined by a relatively large neutron exposure (τ=1.3 mb&lt;sup&gt;-1&lt;/sup&gt;), while an analysis of the rubidium abundance suggests that the s-process occurred at a neutron density of about 2 [x] 10&lt;sup&gt;8&lt;/sup&gt; cm&lt;sup&gt;-3&lt;/sup&gt;.&quot;&lt;ref name=&quot;VVSmith&quot;&gt;{{cite journal
|author=V.V. Smith, K. Cunha, A. Jorissen, and H.M.J. Boffin
|title=Abundances in the symbiotic star AG Draconis: the barium-symbiotic connection
|journal=Astronomy and Astrophysics
|date=November 1996
|volume=315
|issue=11
|pages=179-93
|url=http://adsabs.harvard.edu/abs/1996A%26A...315..179S
|arxiv=
|bibcode=1996A%26A...315..179S
|doi=
|pmid=
|accessdate=2013-09-21 }}&lt;/ref&gt;

The &quot;K giant in AG Dra [has a] ''T''&lt;sub&gt;eff&lt;/sub&gt; ~ 4100 - 4400 K. ... [With a best fit to spectroscopic data of ''T''&lt;sub&gt;eff&lt;/sub&gt; = 4300 K.]&quot;&lt;ref name=&quot;VVSmith&quot;/&gt;

Observed heavy-element abundances may be used &quot;to probe two aspects of the s-process:
# ... the relative abundance distribution of elements analysed ... [determines] the neutron exposure ''τ'' characterizing the s-process efficiency, and
# ... the abundance of Rb ... is sensitive to neutron density [providing] constraints on the s-process neutron density ''N''&lt;sub&gt;n&lt;/sub&gt;.&quot;&lt;ref name=&quot;VVSmith&quot;/&gt;

The &quot;s-process branch point [is] at the ''β''-unstable nucleus &lt;sup&gt;85&lt;/sup&gt;Kr ...
# dominated by &lt;sup&gt;85&lt;/sup&gt;Rb (at 'low' neutron densities) or
# &lt;sup&gt;87&lt;/sup&gt;Rb (at 'high' neutron densities).&quot;&lt;ref name=&quot;VVSmith&quot;/&gt;

Due to the difference &quot;in neutron-capture cross sections&quot; (σ), σ(&lt;sup&gt;85&lt;/sup&gt;Rb)/σ(&lt;sup&gt;87&lt;/sup&gt;Rb) ~ 25, &quot;the s-process abundance of Rb increases dramatically with increasing neutron density. The Rb abundances have been used to infer neutron densities in both
# a small number of barium stars ... and in
# three metal-poor giants of the globular cluster ω Cen.&quot;&lt;ref name=&quot;VVSmith&quot;/&gt;

Comparison shows &quot;a clear and striking increase in the [Rb/Zr] ratio with decreasing [Fe/H] ratio ... is evidence of an increasing s-process neutron density with decreasing metallicity.&quot;&lt;ref name=&quot;VVSmith&quot;/&gt;

Numbers &quot;from Malaney &amp; Lambert (1988) and Malaney (1987a) [can be used] to determine the s-process abundance ratio Rb/Zr as a function of the neutron density ''N''&lt;sub&gt;n&lt;/sub&gt;. ... [First the observed abundances are corrected for previous in flow.] ... ignoring the one extremely Rb-rich ω Cen giant ... The other 8 stars are characterized extremely well by a linear increase of log ''N''&lt;sub&gt;n&lt;/sub&gt; with decreasing [Fe/H]&quot;.&lt;ref name=&quot;VVSmith&quot;/&gt;
{{clear}}

==Protons==
{{main|Radiation astronomy/Protons|Proton astronomy}}
[[Image:3D view of an event recorded with the CMS detector in 2012 at a proton-proton centre of mass energy of 8 TeV.png|thumb|right|250px|3D view of an event recorded with the CMS detector in 2012 at a proton-proton centre of mass energy of 8 TeV. Credit: McCauley, Thomas; Taylor, Lucas; for the CMS Collaboration.{{tlx|free media}}]]
The event shows characteristics expected from the decay of the SM Higgs boson to a pair of photons (dashed yellow lines and green towers). The event could also be due to known standard model background processes.

&quot;As a result of ion irradiation a modification (evolution) of the original target can be generated and new materials can be produced. Bonds in the target material may in fact be broken by energy deposition around the &quot;hot&quot; track of incoming ions. The recombination of fragments produces new and also complex molecules. If carbon is present in the target, even long chain polymer-like substances that are stable above room temperature can be produced ... The presence of organic material in the [solar system], possibly produced by bombarding ions ... seems now well supported by recent findings from space missions as from Voyager at the Uranian system&quot;.&lt;ref name=&quot;Andronico&quot;/&gt;

The &quot;colour of the organic layers [synthesized organic samples of frozen CH&lt;sub&gt;4&lt;/sub&gt; (T ~ 10 K) ice] depends on the amount of energy deposited by the bombarding beam [~ 10&lt;sup&gt;16&lt;/sup&gt; protons (1.5 MeV) cm&lt;sup&gt;-2&lt;/sup&gt; and ~ 10&lt;sup&gt;17&lt;/sup&gt; protons cm&lt;sup&gt;-2&lt;/sup&gt;]. When first extracted after a (relatively) low ion fluence the materials appear yellow, becoming darker and darker if again bombarded at higher doses.&quot;&lt;ref name=&quot;Andronico&quot;&gt;{{cite journal
|author=G. Andronico, G. A. Baratta, F. Spinella, and G. Strazzulla
|title=Optical evolution of laboratory-produced organics - applications to Phoebe, Iapetus, outer belt asteroids and cometary nuclei
|journal=Astronomy and Astrophysics
|date=October 1987
|volume=184
|issue=1-2
|pages=333-6
|url=http://adsabs.harvard.edu/full/1987A%26A...184..333A
|arxiv=
|bibcode=1987A&amp;A...184..333A
|doi=
|pmid=
|accessdate=2013-09-25 }}&lt;/ref&gt;

&quot;The evolution of organics to carbonaceous material induced by ion irradiation is ... a well established phenomenon independent of the type of original carbon containing material.&quot;&lt;ref name=&quot;Andronico&quot;/&gt;
{{clear}}

==Electrons==
{{main|Radiation astronomy/Electrons|Electron astronomy}}
[[Image:Colorized SEM-image of pyrite nanocrystals in ore matrix.tiff|thumb|right|250px|Colorized SEM-image shows pyrite nanocrystals (yellow octahedra) in an ore matrix. Credit: [[c:user:TiberiusRufus|TiberiusRufus]].{{tlx|free media}}]]
&quot;The temperature of yellow coronal regions is ... about 2.5 [x] 10&lt;sup&gt;6&lt;/sup&gt; [K]. ... although some ions Ca XV will exist at lower, as well as higher temperatures.&quot;&lt;ref name=&quot;Kleczek&quot;/&gt;

&quot;The AS prominences [AS in Menzel-Evans' classification [4];] move with velocities exceeding by far the velocities of other types of prominences [7], [8]. As short-living phenomena, they are condensed quickly and the temperature of the coronal gases should rise in the early stages of their condensation. Indeed, the AS prominences use to be allied with yello line emission (λ 5694).&quot;&lt;ref name=&quot;Kleczek&quot;/&gt;

&quot;The yellow line is namely due to the ion Ca XV, according to Edlen's and Waldmeier's identification. ... the line λ 5694 is emitted by &lt;sup&gt;3&lt;/sup&gt;''P''&lt;sub&gt;1&lt;/sub&gt; - &lt;sup&gt;3&lt;/sup&gt;''P''&lt;sub&gt;0&lt;/sub&gt; transition of Ca XV.&quot;&lt;ref name=&quot;Kleczek&quot;/&gt;

&quot;The solar corona is not in thermodynamical equilibrium. In particular, the photo-recombination is compensated with electron impact ionization, while the reverse processes viz. the photoionization and recombination by impact with two electrons are there negligible.&quot;&lt;ref name=&quot;Kleczek&quot;&gt;{{cite journal
|author=J. Kleczek
|title=Temperature of Yellow Coronal Regions
|journal=Bulletin of the Astronomical Institutes of Czechoslovakia
|date= 1957
|volume=8
|issue=
|pages=68-70
|url=http://adsabs.harvard.edu/full/1957BAICz...8...68K
|arxiv=
|bibcode=1957BAICz...8...68K
|doi=
|pmid=
|accessdate=2013-09-26 }}&lt;/ref&gt;
{{clear}}

==Positrons==
{{main|Radiation astronomy/Positrons|Positron astronomy}}
[[Image:TGFantimatter.gif|thumb|right|250px|Simulation of a terrestrial gamma-ray flash (magenta) shows associated electron/positron beams (yellow/green) along a magnetic field line. Credit: NASA's Goddard Space Flight Center.{{tlx|free media}}]]
Calculations of &quot;the changes in the surface chemical composition of intermediate-mass stars in the first phase of convection dredge-up ... has been used to determine the changes in the surface chemical composition of stars with masses 2.5, 5, 10, 20 ''M''&lt;sub&gt;ʘ&lt;/sub&gt; due to nuclear reactions of the pp chains, the triple CNO cycle, and the NeNa and MgAl cycles.&quot;&lt;ref name=&quot;Denisenkov&quot;/&gt;

&quot;We followed the changes that take place in 30 reactions in the abundances of the
electrons, positrons, and 24 nuclides, a complete list of which, together with their initial
abundances (in the proportions of Cameron [i0]), is given in [17].&quot;&lt;ref name=&quot;Denisenkov&quot;&gt;{{cite journal
|author=P. A. Denisenkov
|title=Origin of anomalous sodium abundances in yellow supergiants
|journal= Astrophysics
|date=September-October 1989
|volume=31
|issue=2
|pages=588-97
|url=http://www.springerlink.com/index/UR5K48T7538H0762.pdf
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2013-09-26 }}&lt;/ref&gt;

==Plasma objects==
{{main|Plasmas/Plasma objects}}
[[Image:Yellow and cyan aurora.jpg|thumb|right|300px|This photo of yellow and green auroras shows convincingly that yellow is a distinctive result of the auroral process. Credit: Belinda Witzenhausen.{{tlx|fairuse}}]]
[[Image:NorthernLightsUnusualNewUrengoiRussia.jpg|thumb|left|300px|This image captures an unusual aurora from Urengoi, Russia. Credit: Unknown.{{tlx|fairuse}}]]
[[Image:Alaska2014ColorsVibrations.jpg|thumb|left|300px|This aurora image from Alaska shows distinctive yellow associated with the horizon. Credit: Unknown.{{tlx|fairuse}}]]
[[Image:Yellow Aurora Alaska 2014.jpg|thumb|left|300px|This is another aurora from Alaska containing yellow. Credit: Unknown.{{tlx|fairuse}}]]
[[Image:Beaghmoreaurorafeb27th014-13.jpg|thumb|right|300px|This orange and yellow aurora occurred above Beaghmore Stone Circles. Credit: Martin McKenna.{{tlx|fairuse}}]]
Any doubt that a yellow aurora can occur should be put to rest with the image on the right.

The image on the left shows individual rays of radiation apparently impacting an upper atmospheric layer to produce a bead-like pattern.

The second image down on the left shows yellow of an aurora near the horizon with apparently the midnight Sun off to the left.

The third image on the left contains yellow aurora that is closer to true yellow.

The second image down on the right shows a yellow aurora following the skyline with an orange aurora above.

&quot;On February 25th 2014 a violent X4.9-class solar flare erupted from a large sunspot group which had just rotated into view around the SE limb of the solar disk. The CME it unfurled was a massive full halo feature in the form of an expanding cloud of highly charged particles and plasma en route to the inner planets at a staggering velocity of over 2000km/sec. At this speed the CME would sweep across 93 million miles of space and impact planet Earth in only two days. However there was bad news as the source of this flare - and subsequent CME event - was located so close to the limb of the sun that the CME was very unlikely to impact Earth because it was located too far from the meridian and hence was not termed geoeffective which meant there was no chance of any Earth directed component at all. A few hours later a more detailed look by spaceweather scientists followed which offered some cautious optimism for in some of their forecasting models there was a slight chance that the CME could hit Earth a glancing blow with a possibility of minor geomagnetic storms on Feb 27th however the consensus was that the CME would probably miss entirely or if there was a hit then it wasn't expected to be significant.&quot;&lt;ref name=McKenna&gt;{{ cite book
|author=Martin McKenna
|title=Beaghmore Stone Circles &amp; Lough Fea Crimson Geomagnetic Storm
|publisher=Nightskyhunter
|location=Ireland
|date=27 February 2014
|url=http://www.nightskyhunter.com/Beaghmore%20Stone%20Circles%20Aurora%20-%20Feb%2027th%202014.html
|accessdate=2015-12-01 }}&lt;/ref&gt;

&quot;The B&lt;sub&gt;z&lt;/sub&gt; is the secret to a good aurora show, this is [where] its at, the B&lt;sub&gt;z&lt;/sub&gt; (pronounced Bee Sub Zee) is a value indicating the tilt of the Interplanetary Magnetic Field or IMF. If the B&lt;sub&gt;z&lt;/sub&gt; is N then you can forget about a good show, even if the KP is good it won't make a difference, however if the B&lt;sub&gt;z&lt;/sub&gt; tilts S then the Earth and Sun's magnetic fields become aligned and in effect what you are doing is opening a gate way [...] allowing the highly charged solar particles to interact with the Earth's magnetosphere undisturbed - this open channel will manifest as a strong geomagnetic storm. The fact that it was - 20 got me extremely excited, this value meant the aurora was going to be strong and would be seen from far more southern latitudes than usual.&quot;&lt;ref name=McKenna/&gt;
{{clear}}

==Gaseous objects==
[[Image:IRAS 22036+5306.tif|thumb|right|250px|Close to a bright, nearby star in this image, the bizarre, whorl-shaped object known as IRAS 22036+5306 has been captured during a brief tumultuous period late in a star's life. Credit: NASA/ESA Hubble Space Telescope.{{tlx|free media}}]]
Inside IRAS 22036+5306 lies an aged star that has coughed off almost all of its outer material, forming a cloud in space. Hidden under this veil, the dense, still-burning, exposed core of the star grows hotter. Encircling the star is a torus consisting partly of castoff material, as well as possibly the grainy remnants of comets and other small, rocky bodies. Twin jets spout from the star’s poles and pierce this dusty waist. The jets contain gobbets of material — typically about ten thousand times the mass of the Earth — hurling outwards at a speed of nearly 800 000 kilometres per hour.

IRAS 22036+5306 is making the transition through the protoplanetary, or preplanetary, nebula phase. Only a few hundred such nebulae have been spotted in our galaxy. For now, light from the central star is merely being reflected off its expelled gaseous shell. Soon, however, the star will become a very hot, white dwarf, and its intense ultraviolet radiation will ionise the blown-off gas, making it glow in rich colours. IRAS 22036+5306 will have then blossomed into a fully-fledged planetary nebula, and this event will serve as a last hurrah before the star starts its very slow final cool-down.

Planetary nebulae are much longer-lived than their precursors, protoplanetary nebulae, and are therefore more commonly spotted. The term planetary nebula is a leftover from observations through small telescopes made by early astronomers to whom some of these objects looked circular and similar in appearance to the outer planets Uranus and Neptune.

IRAS 22036+5306 is found about 6500 light-years away in the constellation of Cepheus (The King). 
{{clear}}

==Liquid objects==
[[Image:Golden-sunset.jpg|thumb|right|250px|This picture of the sun is like a golden liquid during sunset. Credit: [[c:user:Madheswaran|Madheswaran]].{{tlx|free media}}]]
A sunset here appears like a golden liquid.
{{clear}}

==Rocky objects==
{{main|Rocks/Rocky objects}}
[[Image:Yellow rocks in Grand Canyon of the Yellowstone.JPG|thumb|right|250px|Sulfur deposits are shown from the Yellowstone Caldera. Credit: [[c:user:Maveric149|Daniel Mayer]].{{tlx|free media}}]]
&quot;Euhedral crystals [from the Lodran meteorite AMNH 314] of olivine and clear pale yellow fragments of orthopyroxene (Opx) and two green grains were examined by precession camera.&quot;&lt;ref name=&quot;Mori&quot;&gt;{{cite journal
|author=H. Mori, Hiroshi Takeda, M. Prinz and G. E. Harlow
|title=Mineralogical and Crystallographic Studies of Lodranite and Primitive Achondrite Groups Bearing on Their Genetic Link
|journal=Lunar and Planetary Science
|date=March 1984
|volume=XV
|issue=
|pages=567-8
|url=http://adsabs.harvard.edu/full/1984LPI....15..567M
|arxiv=
|bibcode=1984LPI....15..567M
|doi=
|pmid=
|accessdate=2013-09-15 }}&lt;/ref&gt;
{{clear}}

==Heliums==
{{main|Chemicals/Heliums}}
[[Image:Helium spectra.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental helium. Credit:[[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
[[Image:M57-spectrum-ru.png|thumb|right|250px|This is a spectrum of Ring Nebula (M57) in range 450.0 — 672.0 nm. Credit: [[c:User:Minami Himemiya|Minami Himemiya]].{{tlx|free media}}]]
&quot;The helium emission lines behave in a qualitatively similar way to the calcium triplet. The 5876 Å line (Fig. 1e) is the dominant line in all the spectra, although two other transitions (6678 and 7065) are also in emission in most of the stars and have nearly identical profiles.&quot;&lt;ref name=&quot;Muzerolle&quot;&gt;{{cite journal
|author=James Muzerolle, Lee Hartmann, and Nuria Calvet
|title=Emission-Line Diagnostics of T Tauri Magnetospheric Accretion. I. Line Profile Observations
|journal=The Astronomical Journal
|date=July 1998
|volume=116
|issue=1
|pages=455-68
|url=http://iopscience.iop.org/1538-3881/116/1/455
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2012-01-23 }}&lt;/ref&gt; He I is 587.6 nm, a yellow emission line. The He I photospheric emission line &quot;narrow component is present in emission ... with [chromospheric] veilings larger than 0.4, being conspicuous even in those heavily veiled stars&quot;.&lt;ref name=&quot;Batalha&quot;&gt;{{cite journal
|author=C. C. Batalha, N. M. Stout-Batalha, G. Basri, and M. A. O. Terra
|title=The Narrow Emission Lines of T Tauri Stars
|journal=The Astrophysical Journal Supplement
|date=March 1996
|volume=103
|issue=3
|pages=211
|url=
|arxiv=
|bibcode=1996ApJS..103..211B
|doi=10.1086/192275
|pmid=
|accessdate=2012-01-23 }}&lt;/ref&gt; The chromospheric veiling apparently results in the emission broadening of the He I emission from the chromosphere which is partially added to the He I narrow emission from the photosphere.&lt;ref name=&quot;Batalha&quot;/&gt;

&quot;The radiative loss for both broad and narrow emission--i.e., the excess of emission over the external continuum expressed in percentages of the photospheric fluxes--is ''F''&lt;sub&gt;ph&lt;/sub&gt;(1 + ν)EW&lt;sub&gt;obs&lt;/sub&gt;, where ''F''&lt;sub&gt;ph&lt;/sub&gt; is the nearby photospheric flux and EW&lt;sub&gt;obs&lt;/sub&gt; is the equivalent width of the observed emission component.&quot;&lt;ref name=&quot;Batalha&quot;/&gt; &quot;[B]y assumption, [the dynamo] controls the narrow component fluxes.&quot;&lt;ref name=&quot;Batalha&quot;/&gt;

In the spectrum at right the yellow He I emission line is detected and recorded at normalized intensities (to the oxygen III line) from the [[w:Ring Nebula|Ring Nebula]].

==Carbons==
[[Image:Carbon Spectra.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental carbon. Credit:[[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
Carbon has one line in the yellow.
{{clear}}

==Nitrogens==
{{main|Chemicals/Nitrogens}}
[[Image:Nitrogen.Spectrum.Vis.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental nitrogen. Credit:[[c:User:Kurgus|Kurgus]].{{tlx|free media}}]]
Nitrogen has a yellow forbidden line, specifically N II at 575.5 nm, that may be used to indicate nitrogen abundances and contribute to nitrogen/oxygen (N/O) abundance gradients. Surveys of [[w:H II region|H II region]]s in [[w:Spiral galaxy|spiral galaxies]] have suggested that N/O abundance ratios increase from outer-arm nebulae to inner-arm nebulae.&lt;ref name=&quot;Searle&quot;&gt;{{cite journal
|author=Leonard Searle
|title=
|journal=The Astrophysical Journal
|date= 1971
|volume=168
|issue=
|pages=327
|url=
|arxiv=
|bibcode=1971ApJ...168..327S
|doi=
|pmid=
|accessdate=2012-03-19 }}&lt;/ref&gt; &quot;Electron temperatures are generally derived from the ratio of auroral to nebular lines in [O III] or [N II].&quot;&lt;ref name=&quot;Hawley&quot;&gt;{{cite journal
|author=S. A. Hawley
|title=The chemical composition of galactic and extragalactic H II regions
|journal=The Astrophysical Journal
|date=September 1, 1978
|volume=224
|issue=9
|pages=417-36
|url=
|arxiv=
|bibcode=1978ApJ...224..417H
|doi=10.1086/156389
|pmid=
|accessdate=2012-03-19 }}&lt;/ref&gt; &quot;[B]ecause of the proximity of strong night-sky lines at λ4358 and λλ5770, 5791, the auroral lines of [O III] λ4363 and [N II] λ5755 are often contaminated.&quot;&lt;ref name=&quot;Hawley&quot;/&gt;

&quot;The nitrogen abundance appears to increase with decreasing galactocentric distance. ... A least-squares solution weighting the points equally gives a magnitude for the gradient ''d''(log N/H)/''d''r = -0.10 ± 0.03 kpc&lt;sup&gt;-1&lt;/sup&gt;.&quot;&lt;ref name=&quot;Hawley&quot;/&gt; &quot;The ratio N/O clearly increases with decreasing ''R''. A least-squares fit to the data ... gives ''d''(log N/O)/''d''r = -0.06 ± 0.02 kpc&lt;sup&gt;-1&lt;/sup&gt;.&quot;&lt;ref name=&quot;Hawley&quot;/&gt;
{{clear}}

==Oxygens==
{{main|Chemicals/Oxygens}}
[[Image:Oxygen spectre.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental oxygen. Credit: [[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
Oxygen has two yellow lines.
{{clear}}

==Fluorines==
[[Image:Figure-9.-The-light-signature-of-Fluorine.png|thumb|center|400px|This diagram contains the emission and absorption lines for the element fluorine. Credit: Alex Petty.{{tlx|fairuse}}]]
Fluorine has several lines in the yellow as shown in the above spectrum.
{{clear}}

==Neons==
[[Image:Neon spectrum visible.png|thumb|center|400px|This is a visual spectrum of neon showing its many emission lines. Credit: [[c:User:McZusatz|McZusatz]].{{tlx|free media}}]]
There is a &quot;bright yellow line of neon X [at] 5852.488 [Å, 585.2488 nm.]&quot;&lt;ref name=&quot;Babcock&quot;&gt;{{cite journal
|author=Harold D. Babcock
|title=A study of the green auroral line by the interference method
|journal=The Astrophysical Journal
|date=May 1923
|volume=57
|issue=05
|pages=209-21
|url=http://adsabs.harvard.edu/full/1923ApJ....57..209B
|arxiv=
|bibcode=1923ApJ....57..209B
|doi=10.1086/142747
|pmid=
|accessdate=2013-01-18 }}&lt;/ref&gt;
{{clear}}

==Sodiums==
[[Image:Sodium spectrum visible.png|center|thumb|400px|Sodium spectrum is ringrising 400 nm - 700 nm Credit: [[c:user:McZusatz|McZusatz]].{{tlx|free media}}]]
Fraunhofer's original (1817) designations of absorption lines in the solar spectrum
{| {{széptáblázat}}
 ! [[w:Letter (alphabet)|Letter]]
 ! [[Wavelength]] ([[w:nanometer|nm]])
 ! Chemical origin
 ! Colour range
 |-
 | {{center top}}A{{center bottom}}
 | {{center top}}759.37{{center bottom}}
 | {{center top}}atmospheric [[w:oxygen|O&lt;sub&gt;2&lt;/sub&gt;]]{{center bottom}}
 | {{center top}}dark red{{center bottom}}
 |-
 | {{center top}}B{{center bottom}}
 | {{center top}}686.72{{center bottom}}
 | {{center top}}atmospheric [[w:oxygen|O&lt;sub&gt;2&lt;/sub&gt;]]{{center bottom}}
 | {{center top}}red{{center bottom}}
 |-
 | {{center top}}C{{center bottom}}
 | {{center top}}656.28{{center bottom}}
 | {{center top}}[[hydrogen]] alpha{{center bottom}}
 | {{center top}}red{{center bottom}}
 |-
 | {{center top}}D1{{center bottom}}
 | {{center top}}589.59{{center bottom}}
 | {{center top}}neutral [[w:sodium|sodium]]{{center bottom}}
 | {{center top}}red orange{{center bottom}}
 |-
 | {{center top}}D2{{center bottom}}
 | {{center top}}589.00{{center bottom}}
 | {{center top}}neutral [[w:sodium|sodium]]{{center bottom}}
 | {{center top}}yellow{{center bottom}}
 |-
 | {{center top}}E{{center bottom}}
 | {{center top}}526.96{{center bottom}}
 | {{center top}}neutral [[w:iron|iron]]{{center bottom}}
 | {{center top}}green{{center bottom}}
 |-
 | {{center top}}F{{center bottom}}
 | {{center top}}486.13{{center bottom}}
 | {{center top}}[[hydrogen]] beta{{center bottom}}
 | {{center top}}cyan{{center bottom}}
 |-
 | {{center top}}G{{center bottom}}
 | {{center top}}431.42{{center bottom}}
 | {{center top}}CH [[w:molecule|molecule]]{{center bottom}}
 | {{center top}}blue{{center bottom}}
 |-
 | {{center top}}H{{center bottom}}
 | {{center top}}396.85{{center bottom}}
 | {{center top}}ionised [[w:calcium|calcium]]{{center bottom}}
 | {{center top}}dark violet{{center bottom}}
 |-
 | {{center top}}K{{center bottom}}
 | {{center top}}393.37{{center bottom}}
 | {{center top}}ionised [[w:calcium|calcium]]{{center bottom}}
 | {{center top}}dark violet&quot;{{center bottom}}
 |}

Sodium produces two spectral lines known as D1 and D2, or the &quot;sodium doublet&quot;. Their average wavelength, 589.3 nm, is often just called &quot;D&quot;.

'''Def.''' &quot;[a] [[wikt:street lamp|street lamp]] in which [[wikt:electricity|electricity]] is passed through sodium vapour to emit a yellow [[wikt:light|light]]&quot;, from Wiktionary [[wikt:sodium vapor lamp|sodium vapor lamp]], is called a '''sodium vapor lamp'''.
{{clear}}

==Calciums==
[[Image:Calcium spectrum visible.png|thumb|center|400px|Calcium spectrum is 400 nm - 700 nm. Credit: [[c:user:McZusatz|McZusatz]].{{tlx|free media}}]]
During the limb flares of December 18, 1956, a coronal line at 569.4 nm, a yellow line, occurred at 1822 UTC, 1900 UTC, undiminished up to 20,000 km above the solar limb, and at 2226 UTC, is identified as Ca XV.&lt;ref name=&quot;Zirin59&quot;&gt;{{cite journal
|author=Harold Zirin
|title=Physical Conditions in Limb Flares and Active Prominences. II. a Remarkable Limb Flare, December 18, 1956
|journal=Astrophysical Journal
|date=March 1959
|volume=129
|issue=3
|pages=414-23
|url=
|bibcode=1959ApJ...129..414Z
|doi= 10.1086/146633
|pmid=
|accessdate=2011-08-01 }}&lt;/ref&gt; &quot;The coronal temperature was 4000000°.&quot;&lt;ref name=&quot;Zirin59&quot;/&gt; &quot;The December 18, 1956, flare appears to have been a violent condensation of material from a dense [[coronal cloud]] above an active region.&quot;&lt;ref name=&quot;Zirin59&quot;/&gt;
{{clear}}

==Alloys==
{{main|Radiation astronomy/Alloys}}
[[Image:Microstructure of rolled and annealed brass; magnification 400X.jpg|thumb|right|250px|Microstructure of rolled and annealed brass is shown at magnification 400X. Credit: [[c:user:Strangerhahaha|Strangerhahaha]].{{tlx|free media}}]]
The earliest brasses may have been natural alloys made by [[w:smelting|smelting]] zinc-rich copper [[w:ores|ores]].&lt;ref name=&quot;Craddock&quot;&gt;Craddock, P.T. and Eckstein, K (2003) &quot;Production of Brass in Antiquity by Direct Reduction&quot; in Craddock, P.T. and Lang, J. (eds) ''Mining and Metal Production Through the Ages'' London: British Museum pp. 226–7&lt;/ref&gt;
{{clear}}

==Sun==
{{main|Stars/Sun|Sun (star)}}
[[Image:Sun920607.jpg|thumb|right|180px|This is a visual image of the Sun with some sunspots visible. The two small spots in the middle have about the same diameter as our planet Earth. Credit: NASA.{{tlx|free media}}]]
[[Image:Sun Atmosphere Temperature and Density SkyLab.jpg|thumb|200 px|This graph shows the temperature and density of the Sun's atmosphere from Skylab observations. Credit: John A. Eddy, NASA.{{tlx|free media}}]]
A natural division of astronomical bodies, or objects, between '''rocky bodies''', astronomical objects with solid surfaces, or solids and liquids predominately on the surface, and '''gas bodies''', astronomical objects with gases predominately detected and apparently constituting a surface, may be an informative approach toward [[stellar science]].

Depending primarily upon gas temperature, the presence of gas may be used to determine the composition of the gas body observed, at least the outer layer. Early spectroscopy&lt;ref name=&quot;Russell&quot;&gt;{{cite journal
|author=H. N. Russell
|title=
|journal=The Astrophysical Journal
|date= 1929
|volume=70
|issue=
|pages=11-82
|url=
|arxiv=
|bibcode=1929ApJ....70...11R
|doi=
|pmid=
|accessdate=2012-07-06 }}&lt;/ref&gt; of the Sun using estimates of &quot;the line intensities of several lines by eye [to derive] the abundances of ... elements ... [concluded] that the Sun [is] largely made of hydrogen.&quot;&lt;ref name=&quot;Basu&quot;&gt;{{cite journal
|author=Sarbani Basu and H. M. Antia
|title=HelioseismologyandSolarAbundances
|journal=Physics Reports
|date=March 2008
|volume=457
|issue=5-6
|pages=217-83
|url=
|arxiv=0711.4590
|bibcode=2008PhR...457..217B
|doi=10.1016/j.physrep.2007.12.002
|pmid=
|accessdate=2012-07-06 }}&lt;/ref&gt;

The second image at right describes graphically the temperature and density of the Sun's atmosphere from the photosphere upwards. &quot;The Sun's photosphere has a temperature between 4500 and 6000 [[w:kelvin|K]]&lt;ref&gt;[http://imagine.gsfc.nasa.gov/docs/science/know_l1/sun.html The Sun - Introduction]&lt;/ref&gt; (with an effective temperature of 5777 K) and a [[w:density|density]] of about [2 x 10&lt;sup&gt;-4&lt;/sup&gt;[[w:kilogram|kg]]/[[w:cubic meter|m&lt;sup&gt;3&lt;/sup&gt;]];&lt;ref name=&quot;nasa&quot;&gt;{{cite book
| url=http://history.nasa.gov/SP-402/p2.htm
| title=SP-402 A New Sun: The Solar Results From Skylab }}&lt;/ref&gt; other stars may have hotter or cooler photospheres. The Sun's photosphere is composed of [[w:convection cell|convection cell]]s called [[w:Granule (solar physics)|granules]]—cells of gas each approximately 1000 km in diameter&lt;ref&gt;{{cite book
| url=http://solarscience.msfc.nasa.gov/feature1.shtml| title=NASA/Marshall Solar Physics| publisher=NASA}}&lt;/ref&gt; with hot rising gas in the center and cooler gas falling in the narrow spaces between them. Each granule has a lifespan of only about eight minutes, resulting in a continually shifting &quot;boiling&quot; pattern. Grouping the typical granules are super granules up to 30,000 kilometers in diameter with lifespans of up to 24 hours. These details are too fine to see on other stars.
{{clear}}

==Mercury==
{{main|Liquids/Liquid objects/Mercury}}
[[Image:PIA19411-Mercury-WaterIce-Radar-MDIS-Messenger-20150416.jpg|thumb|right|250px|This orthographic projection view provides a look at Mercury's north polar region. Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington.{{tlx|free media}}]]
This orthographic projection view provides a look at Mercury's north polar region. The yellow regions in many of the craters mark locations that show evidence for water ice, as detected by Earth-based radar observations from Arecibo Observatory in Puerto Rico. MESSENGER has collected compelling new evidence that the deposits are indeed water ice, including imaging within the permanently shaded interiors of some of the craters, such as Prokofiev and Fuller.

Instrument: Mercury Dual Imaging System (MDIS) Arecibo Radar Image: In yellow (Harmon et al., 2011, Icarus 211, 37-50).

&quot;[H]igh-resolution spectral measurements of Mercury show emission in sodium D lines (Potter and Morgan 1985a). This suggests a substantial sodium population in Mercury's atmosphere ... possibly due to photo-sputtering of the planetary surface&quot;.&lt;ref name=&quot;CTRussell&quot;&gt;{{cite book
|author=C. T. Russell, D. N. Baker and J. A. Slavin
|title=The Magnetosphere of Mercury, In: ''Mercury''
|publisher=University of Arizona Press
|location=Tucson, Arizona, United States of America
|date=January 1, 1988
|editor=Faith Vilas
|editor2=Clark R. Chapman
|editor3=Mildred Shapley Matthews
|pages=514-61
|url=http://www-ssc.igpp.ucla.edu/personnel/russell/papers/magMercury.pdf
|arxiv=
|bibcode=1988merc.book..514R
|doi=
|isbn=0816510857
|pmid=
|accessdate=2012-08-23 }}&lt;/ref&gt;
{{clear}}

==Venus==
{{main|Gases/Gaseous objects/Venus}}
[[Image:Venus2 mag big.png|thumb|right|250px|Using an imaging radar technique, the Magellan spacecraft was able to lift the veil from the face of Venus and produce this spectacular high resolution image of the planet's surface. Red, in this false-color map, represents mountains, while blue represents valleys. Credit: Magellan Team, JPL, NASA.{{tlx|free media}}]]
Using an imaging radar technique, the Magellan spacecraft was able to lift the veil from the Face of Venus and produce this spectacular high resolution image of the planet's surface. Red, in this false-color map, represents mountains, while blue represents valleys. This 3-kilometer resolution map is a composite of Magellan images compiled between 1990 and 1994. Gaps were filled in by the Earth-based Arecibo Radio Telescope. The large yellow/red area in the north is Ishtar Terra featuring Maxwell Montes, the largest mountain on Venus. The large highland regions are analogous to continents on Earth.

&quot;Selected images of Venus [show] cloud configurations in yellow light&quot;.&lt;ref name=&quot;Dollfus&quot;&gt;{{cite journal
|author=A Dollfus
|title=History of planetary science. The Pic du Midi planetary observation Project: 1941–1971
|journal=Planetary and Space Science
|date=August 1, 1998
|volume=46
|issue=8
|pages=1037-73
|url=http://www.sciencedirect.com/science/article/pii/S0032063398000348
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2013-09-14 }}&lt;/ref&gt; These images are photographs taken between October 3, 1943, and March 14, 1945.&lt;ref name=&quot;Dollfus&quot;/&gt;
{{clear}}

==Earth==
{{main|Rocks/Rocky objects/Earth}}
[[Image:Sahara satellite hires.jpg|thumb|right|250px|The image shows the Sahara desert from space. Credit: NASA.{{tlx|free media}}]]
&quot;Spectral properties of certain palagonitic soils found on Mauna Kea, Hawaii are similar to the spectral properties measured by earth-based telescopes for Martian soils [1,2,3]. ... Three layers with distinctly different colors (upper red, middle black, lower yellow) were sampled from hydrothermally altered basaltic tephra just below the summit of Mauna Kea.&quot;&lt;ref name=&quot;Golden&quot;&gt;{{cite journal
|author=D. C. Golden, R. V. Morris, D. W. Ming, R. K. Vempati, and H. V. Lauer
|title=Mineralogy of Palagonitic Soils from Hawaii
|journal=Abstracts of the Lunar and Planetary Science Conference
|date=March 1991
|volume=22
|issue=03
|pages=449-50
|url=http://adsabs.harvard.edu/abs/1991LPI....22..449G
|arxiv=
|bibcode=1991LPI....22..449G
|doi=
|pmid=
|accessdate=2013-09-14 }}&lt;/ref&gt;

&quot;The clay fractions (&lt; 2 µm) of three palagonite samples-MK11 (red), MK12 (black), and MK13 (yellow) collected at an elevation of 4145 meters near the summit of Mauna Kea volcano in Hawaii ... The fine fractions of the black (MK12) and yellow (MK13) samples were similar to those of martian bright regions in terms of their overall shape.&quot;&lt;ref name=&quot;Golden92&quot;&gt;{{cite journal
|author=D. C. Golden, D. W. Ming, R. V. Morris and H. V. Lauer Jr.
|title=Mars surface weathering products and spectral analogs: Palagonites and synthetic iron minerals, In: ''Workshop on the Martian Surface and Atmosphere Through Time''
|publisher=Lunar and Planetary Institute
|location=
|date=December 1992
|editor=
|pages=59-60
|url=http://adsabs.harvard.edu/full/1992msat.work...59G
|arxiv=
|bibcode=1992msat.work...59G
|doi=
|pmid=
|isbn=
|accessdate=2013-09-15 }}&lt;/ref&gt;

At right is a composite image of the Sahara. Most of the images are from the MODIS imager onboard the Terra satellite.
{{clear}}

==Moon==
{{main|Liquids/Liquid objects/Moon}}
[[Image:Full moon - Flickr - GeorgeTan.jpg|thumb|right|250px|Big orange-yellowish moon is always observed on the 15th of each lunar month. Credit: [https://www.flickr.com/people/171425013@N02 GeorgeTan # 2...thanks for millionth support from Singapore].{{tlx|free media}}]]
&quot;There is ... a dearth of basalt compositions corresponding to differentiates of the yellow glasses. ... After olivine and chromite, differentiates of the Apollo 14 and 17 yellow glass magmas should differ only slightly in crystallization sequence. ... For green and yellow glasses, liquids are saturated only with olivine and chromite; for red and black glasses, negative slope represents liquids saturated with olivine and chromite, positive slope indicates olivine, chromite, and armalcolite.&quot;&lt;ref name=&quot;Longhi&quot;&gt;{{cite journal
|author=J. Longhi
|title=Differentiates of the Picritic Glass Magmas: The Missing Mare Basalts, In: ''Workshop on Lunar Volcanic Glasses: Scientific and Resource Potential''
|publisher= Lunar and Planetary Institute
|location=Houston, TX, USA
|date= 1990
|editor=John W. Delano and Grant H. Heiken
|pages=46-7
|url=http://adsabs.harvard.edu/full/1990lgvp.work...46L
|arxiv=
|bibcode=1990lgvp.work...46L
|doi=
|pmid=
|isbn=
|accessdate=2013-09-15 }}&lt;/ref&gt;

&quot;An unusual yellowish glass is found in the interstices, in fracture fillings, and as encrustations of a few uncommon, mildly fragmented KREEP basalt particles in Apollo 15 soils.&quot;&lt;ref name=&quot;ABasu&quot;&gt;{{cite journal
|author=Abhijit Basu
|title=Origin of Yellow Glasses Associated with Apollo 15 KREEP Basalt Fragments
|journal=Proceedings of Lunar and Planetary Science
|date= 1992
|volume=22
|issue=
|pages=365-72
|url=http://adsabs.harvard.edu/full/1992LPSC...22..365B
|arxiv=
|bibcode=1992LPSC...22..365B
|doi=
|pmid=
|accessdate=2013-09-15 }}&lt;/ref&gt;

Ferrobasalts in the Apollo 11 specimens have yellow materials present. &quot;Irregular fragments of vesicular glass, pale yellow to golden brown are abundant. Some are up to half a millimeter across.&quot;&lt;ref name=&quot;Smith1970&quot;&gt;{{cite journal
|author=J. V. Smith, A. T. Anderson, R. C. Newton, E. J. Olsen, A. V. Isaacson
|title=Petrologic history of the moon inferred from petrography, mineralogy and petrogenesis of Apollo 11 rocks
|journal=Geochimica et Cosmochimica Acta Supplement
|date= 1970
|volume=1
|issue=
|pages=897-925
|url=http://adsabs.harvard.edu/full/1970GeCAS...1..897S
|arxiv=
|bibcode=1970GeCAS...1..897S
|doi=
|pmid=
|accessdate=2013-09-16 }}&lt;/ref&gt;
{{clear}}

==Mars==
{{main|Liquids/Liquid objects/Mars}}
[[Image:Mars sky at noon PIA01546.jpg|thumb|right|250px|The Martian sky at noon is yellow-brown, which contrasts with its pinkish-red color at sunset. Credit: NASA/JPL-Caltech.{{tlx|free media}}]]
The true color of Mars based upon three filters with the sky set to a luminance of 60. The color of the Pathfinder landing site is yellowish brown with only subtle variations. These colors are identical to the measured colors of the Viking landing sites reported by Huck et al. [1977]. This image was taken near local noon on Sol 10.

&quot;The most striking change in the nontronite was color. The original nontronite was olive-yellow, corresponding to 25.Y 6/6 in the Munsell color chart (3). The material shocked to 180 kbar turned yellow-brown, 1.0Y 5/6, and the nontronite brought to 300 kbar was strong brown, 7.5Y 4/6.&quot;&lt;ref name=&quot;Weldon&quot;/&gt;

&quot;[L]ittle Fe&lt;sup&gt;+2&lt;/sup&gt; (... is the case for most yellow nontronites).&quot;&lt;ref name=&quot;Weldon&quot;&gt;{{cite journal
|author=Ray J. Weldon, Mark B. Boslough, and T. J. Ahrens
|title=Shock-Induced Color Changes in Nontronite: A Possible Martian Surface Process
|journal=Lunar and Planetary
|date=March 1980
|volume=6
|issue=03
|pages=1234-5
|url=http://adsabs.harvard.edu/full/1980LPI....11.1234W
|arxiv=
|bibcode=1980LPI....11.1234W
|doi=
|pmid=
|accessdate=2013-09-14 }}&lt;/ref&gt;
{{clear}}

==Io==
{{main|Volcanoes/Io|Rocks/Rocky objects/Io}}
[[Image:Iosurface gal.jpg|thumb|right|250px|Io, the most volcanic body in the solar system, is seen in the highest resolution obtained to date by NASA's Galileo spacecraft. Credit: NASA.{{tlx|free media}}]]
[[Image:PIA01667-Io's Pele Hemisphere After Pillan Changes.jpg|thumb|right|250px|This global view of Io, is obtained from the tenth orbit of Jupiter by NASA's Galileo spacecraft. Credit: NASA.{{tlx|free media}}]]
[[Image:Io, moon of Jupiter, NASA.jpg|thumb|right|250px|This image of Io continues to the left around the rocky object. Credit: NASA.{{tlx|free media}}]]
[[Image:Io (north pole) from Galileo and Voyager missions.jpg|thumb|right|250px|This composite of images from Galileo and Voyager 1 shows Io's north pole. Credit: U.S. Geological Survey and NASA.{{tlx|free media}}]]
[[Image:Io (south pole) from Galileo and Voyager missions.jpg|thumb|right|250px|This composite is of Io's south pole. Credit: U.S. Geological Survey and NASA.{{tlx|free media}}]]
[[Image:Iorotateing1day.ogv|thumb|right|250px|In the same way that the Moon always has the same side facing Earth, Io always has the same side facing Jupiter. Credit: U.S. Geological Survey and NASA.{{tlx|free media}}]]
'''Io''' is the innermost of the four Galilean moons of the planet [[Jupiter]] and, with a diameter of 3,642 kilometres (2,263 mi), the fourth-largest moon in the [[Solar System]]. With over 400 active volcanoes, Io is the most geologically active object in the Solar System.&lt;ref name=&quot;book&quot;&gt;{{cite book|title=Encyclopedia of the Solar System|chapter=Io: The Volcanic Moon|author=Rosaly MC Lopes|publisher=Academic Press |year=2006|editor=Lucy-Ann McFadden
|editor2=Paul R. Weissman
|editor3=Torrence V. Johnson|pages=419–431
|url=https://books.google.com/books?isbn=0080474985
|isbn=978-0-12-088589-3}}&lt;/ref&gt;&lt;ref name=&quot;Lopes2004&quot;&gt;{{cite journal |title=Lava lakes on Io: Observations of Io’s volcanic activity from Galileo NIMS during the 2001 fly-bys |journal=Icarus |last=Lopes |first=R. M. C. |coauthors=''et al.'' |pages=140–174 |volume=169 |issue= 1|year=2004
|doi=10.1016/j.icarus.2003.11.013
|bibcode=2004Icar..169..140L}}&lt;/ref&gt; Most of Io's surface is characterized by extensive plains coated with sulfur and sulfur dioxide frost. Io's volcanism is responsible for many of the satellite's unique features. Its volcanic plumes and lava flows produce large surface changes and paint the surface in various shades of yellow, red, white, black, and green, largely due to allotropes and compounds of sulfur.

In the image at right, the smallest features that can be discerned are 2.5 kilometers in size. There are rugged mountains several kilometers high, layered materials forming plateaus, and many irregular depressions called volcanic calderas. Several of the dark, flow-like features correspond to hot spots, and may be active lava flows. There are no landforms resembling impact craters, as the volcanism covers the surface with new deposits much more rapidly than the flux of comets and asteroids can create large impact craters. The picture is centered on the side of Io that always faces away from Jupiter; north is to the top.

Color images acquired on September 7, 1996 have been merged with higher resolution images acquired on November 6, 1996 by the Solid State Imaging (CCD) system aboard NASA's Galileo spacecraft. The color is composed of data taken, at a range of 487,000 kilometers, in the near-infrared, green, and violet filters and has been enhanced to emphasize the extraordinary variations in color and brightness that characterize Io's face. The high resolution images were obtained at ranges which varied from 245,719 kilometers to 403,100 kilometers.

The second image at right is a global view of Jupiter's moon, Io, obtained during the tenth orbit of Jupiter by NASA's Galileo spacecraft. Io, which is slightly larger than Earth's moon, is the most volcanically active body in the solar system. In this enhanced color composite, deposits of sulfur dioxide frost appear in white and grey hues while yellowish and brownish hues are probably due to other sulfurous materials. Bright red materials, such as the prominent ring surrounding Pele, and &quot;black&quot; spots with low brightness mark areas of recent volcanic activity and are usually associated with high temperatures and surface changes. One of the most dramatic changes is the appearance of a new dark spot (upper right edge of Pele), 400 kilometers (250 miles)in diameter which surrounds a volcanic center named Pillan Patera. The dark spot did not exist in images obtained 5 months earlier, but Galileo imaged a 120 kilometer (75 mile) high plume erupting from this location during its ninth orbit. North is to the top of the picture which was taken on September 19, 1997 at a range of more than 500,000 kilometers (310,000 miles) by the Solid State Imaging (SSI) system on NASA's Galileo spacecraft.

The third image at right continues around Io to the left.

The fourth image is of Io's north pole. The new basemap and the polar images of Jupiter's moon Io was produced by combining the best images from both the Voyager 1 and Galileo Missions. Although the subjovian hemisphere of Io was poorly seen by Galileo, superbly detailed Voyager 1 images cover longitudes from 240 W to 40 W and the nearby southern latitudes. A monochrome mosaic of the highest resolution images from both Galileo and Voyager 1 was assembled that includes 51 Voyager 1 images with spatial resolutions sometimes exceeding the 1 km/pixel scale of the final mosaic. Because this mosaic is made up of images taken at various local times of day, care must be taken to note the solar illumination direction when deciding whether topographic features display positive or negative relief. In general, the illumination is from the west over longitudes 40 to 270 W, and from the east over longitudes 270 W to 40 W. Color information was later superimposed from Galileo low phase angle violet, green, and near-infrared (756 nanometer wavelength) images. The Galileo SSI camera's silicon CCD was sensitive to longer wavelengths than the vidicon cameras of Voyager, so that distinctions between red and yellow hues can be more easily discerned. The &quot;true&quot; colors that would be visible to the eye are similar but much more muted than shown here. Image resolutions range from 1 to 10 km/pixel along the equator, with the poorest coverage centered on longitude 50 W.

The fifth image is of Io's south pole.

The last image is an animated image showing a 1 Io day of rotation. &quot;In the same way that the Moon always has the same side facing Earth, Io always has the same side facing Jupiter. The movie shows two speeded-up rotations of Io (a single rotation really takes 1.77 days), and begins with a view of the Jupiter-facing hemisphere. With rotation in an easterly direction, after two seconds the volcano Prometheus (on the equator) comes into view. The massive red deposit around Pele (seconds 5-10) is the most distinctive expression of volcanic activity on Io, and just to the north-west is the horse shoe-shaped Loki Patera, the most powerful volcano on Io. The animation was made using a computer program that wrapped the Io mosaic around a sphere to produce a globe. In all, 360 images were used, each differing by one degree in longitude from the previous image.
{{clear}}

==Stars==
{{main|Stars}}
[[Image:VLTI Revisits the Largest Yellow Hypergiant Ever Discovered (36738658824).jpg|thumb|right|250px|It may not look like much, but this blob shows a remarkable star named V766 Centauri (V766 Cen for short) and its close companion. Credit: European Southern Observatory.{{tlx|free media}}]]
A few years ago using ESO's Very Large Telescope Interferometer (VLTI) V766 Centauri was found to be something known as a yellow hypergiant, a massive and luminous type of star that is extremely rare — and extremely big! Measuring over 1400 times the diameter of the Sun, V766 Cen was not only the largest star of its type ever discovered, but also one of the ten largest stars ever found.

The Secchi Class II consists of yellow stars with evident metallic lines.

&quot;The Harvard classification system is a one-dimensional classification scheme. Stars vary in surface temperature from about 2,000 to 40,000 kelvins. Physically, the classes indicate the temperature of the star's atmosphere and are normally listed from hottest to coldest, as is done in the following table:
{| class=&quot;wikitable&quot;
! Class
! Temperature&lt;ref name=&quot;Habets&quot;/&gt;&lt;br&gt;K
! abbr=&quot;color&quot; | Conventional color
! abbr=&quot;color&quot; | Apparent color&lt;ref name=&quot;Moore&quot;&gt;The Guinness book of astronomy facts &amp; feats, Patrick Moore, 1992, 0-900424-76-1&lt;/ref&gt;&lt;ref name=&quot;Senior&quot;&gt;{{cite book
| date = 2004-12-21
| url = http://outreach.atnf.csiro.au/education/senior/astrophysics/photometry_colour.html
| title = The Colour of Stars
| publisher = Australia Telescope Outreach and Education
| accessdate = 2007-09-26
}}&amp;nbsp;— Explains the reason for the difference in color perception.&lt;/ref&gt;&lt;ref name=&quot;Charity&quot;&gt;[http://www.vendian.org/mncharity/dir3/starcolor/ What color are the stars?], Mitchell Charity. Accessed online March 19, 2008.&lt;/ref&gt;
! Mass&lt;ref name=&quot;Habets&quot;&gt;Tables VII, VIII, Empirical bolometric corrections for the main-sequence, G. M. H. J. Habets and J. R. W. Heinze, ''Astronomy and Astrophysics Supplement Series'' '''46''' (November 1981), pp. 193–237, bibcode=1981A&amp;AS...46..193H. Luminosities are derived from M&lt;sub&gt;bol&lt;/sub&gt; figures, using M&lt;sub&gt;bol&lt;/sub&gt;(ʘ)=4.75.&lt;/ref&gt;&lt;br&gt;(solar masses, M&lt;sub&gt;ʘ&lt;/sub&gt;)
! Radius&lt;ref name=&quot;Habets&quot;/&gt;&lt;br&gt;(solar radii, R&lt;sub&gt;ʘ&lt;/sub&gt;)
! Luminosity&lt;ref name=&quot;Habets&quot;/&gt;&lt;br&gt;(bolometric, L&lt;sub&gt;ʘ&lt;/sub&gt;)
! Hydrogen&lt;br&gt;lines
! Fraction of all&lt;br&gt;[[w:main sequence star|main sequence star]]s&lt;ref name=&quot;LeDrew2001&quot;&gt;{{cite journal
|author=Glenn LeDrew
|bibcode=2001JRASC..95...32L
|title=The Real Starry Sky
|journal=Journal of the Royal Astronomical Society of Canada
|date=February 2001
|volume=95
|issue=1 (whole No. 686, February 2001)
|pages=32–33. ''Note:'' Table 2 has an error and so this article will use 824 as the assumed correct total of main-sequence stars }}&lt;/ref&gt;
|- style=&quot;background:#9bb0ff;&quot;
!style=&quot;background:#9bb0ff;&quot;| [[#Class O|O]]
| ≥&amp;nbsp;33,000&amp;nbsp;K
| style=&quot;background:#9aafff;&quot; | blue
| style=&quot;background:#9bb0ff;&quot; | blue
| ≥&amp;nbsp;16
| ≥&amp;nbsp;6.6
| ≥&amp;nbsp;30,000
| Weak
| ~0.00003%
|- style=&quot;background:#aabfff;&quot;
!style=&quot;background:#abbfff;&quot;| [[#Class B|B]]
| 10,000–33,000&amp;nbsp;K
| style=&quot;background:#cad7ff;&quot; | blue to blue white
| style=&quot;background:#aabfff;&quot; | blue white
| 2.1–16
| 1.8–6.6
| 25–30,000
| Medium
| 0.13%
|- style=&quot;background:#cad7ff;&quot;
!style=&quot;background:#cad7ff;&quot;| [[#Class A|A]]
| 7,500–10,000&amp;nbsp;K
| style=&quot;background:#f8f7ff;&quot; | white
| style=&quot;background:#cad7ff;&quot; | white to blue white
| 1.4–2.1
| 1.4–1.8
| 5–25
| [[w:Strong (relative detectability)|Strong]]
| 0.6%
|- style=&quot;background:#f8f7ff;&quot;
!style=&quot;background:#f8f7ff;&quot;| [[#Class F|F]]
| 6,000–7,500&amp;nbsp;K
| style=&quot;background:#FCFFD3;&quot; | yellowish white
| style=&quot;background:#f8f7ff;&quot; | white
| 1.04–1.4
| 1.15–1.4
| 1.5–5
| Medium
| 3%
|- style=&quot;background:#fff4ea;&quot;
!style=&quot;background:#fff4ea;&quot;| [[#Class G|G]]
| 5,200–6,000&amp;nbsp;K
| style=&quot;background:#fff2a1;&quot; | yellow
| style=&quot;background:#Fff4ea;&quot; | yellowish white
| 0.8–1.04
| 0.96–1.15
| 0.6–1.5
| Weak
| 7.6%
|- style=&quot;background:#ffd2a1;&quot;
!style=&quot;background:#ffd2a1;&quot;| [[#Class K|K]]
| 3,700–5,200&amp;nbsp;K
| style=&quot;background:#FFA351;&quot; | orange
| style=&quot;background:#Ffd2a1;&quot; | yellow orange
| 0.45–0.8
| 0.7–0.96
| 0.08–0.6
| Very weak
| 12.1%
|- style=&quot;background:#ffcc6f;&quot;
!style=&quot;background:#ffcc6f;&quot;| [[#Class M|M]]
| ≤&amp;nbsp;3,700&amp;nbsp;K
| style=&quot;background:#FF6151; color:#FFFFFF&quot; | red
| style=&quot;background:#ffcc6f;&quot; | orange red
| ≤&amp;nbsp;0.45
| ≤&amp;nbsp;0.7
| ≤&amp;nbsp;0.08
| Very weak
| 76.45%
|}

[[Stars]] of [[w:spectral class|spectral class]]es F and G, such as our sun ''Sol'', have [[w:color temperature|color temperature]]s that make them look &quot;yellowish&quot;.&lt;ref name=&quot;Miller&quot;&gt;{{cite book
 | title = Stars and Galaxies
 | author = Ron Miller
 | publisher = Twenty-First Century Books
 | year = 2005
 | isbn = 9780761334668
 | page = 22
 | url = http://books.google.com/?id=QL9uAfad1ggC&amp;pg=PA22 }}&lt;/ref&gt; The first astronomer to classify stars according to their color was [[w:Friedrich Georg Wilhelm von Struve|F. G. W. Struve]] in 1827. One of his classifications was ''flavae'', or yellow, and this roughly corresponded to stars in the modern spectral range F5 to K0.&lt;ref name=&quot;Murdin&quot;&gt;{{cite book
 | author=Paul Murdin
| year=1984
| page=18
 | title=Colours of the stars
| publisher=CUP Archive
|url=https://books.google.com/books?isbn=052125714X
 | isbn=052125714X }}&lt;/ref&gt; The [[w:Strömgren photometric system|Strömgren photometric system]] for stellar classification includes a 'y' or yellow filter that is centered at a wavelength of 550&amp;nbsp;nm and has a bandwidth of 20–30&amp;nbsp;nm.&lt;ref name=&quot;Stromgren&quot;&gt;{{cite journal
 | author=Bengt Strömgren
 | title=Main Sequence Stars, Problems of Internal Constitution and Kinematics (George Darwin Lecture)
 | journal=Quarterly Journal of the Royal Astronomical Society
| volume=8
| pages=8–37 |
bibcode=1963QJRAS...4....8S }}&lt;/ref&gt;&lt;ref name=&quot;Norton&quot;&gt;{{cite book
 | author=Andrew Norton, W. Alan Cooper
 | title=Observing the universe: a guide to observational astronomy and planetary science
 | publisher=Cambridge University Press
| year=2004
 | isbn=0521603935
| page=63
|url=https://books.google.com/books?isbn=0521603935 }}&lt;/ref&gt;

==Yellow degenerates==
[[Image:Van Maanen's star.gif|thumb|right|250px|The image is an optical negative centered on the SIMBAD coordinates J2000.0 for Van Maanen's star. Image is from the Palomar 48-inch Schmidt reflecting telescope. Van Maanen's star is the largest black dot center top right. Credit: NASA/IPAC Extragalactic Database.{{tlx|free media}}]]
[[Image:HR-diag-no-text-2.svg|thumb|left|250px|This is an Hertzsprung-Russell diagram. Note that luminosity class VII has color class G stars within. Credit: [[c:User:Spacepotato|Spacepotato]].{{tlx|free media}}]]
[[Image:GJ 3223 Yellow degenerate.jpeg|thumb|right|250px|GJ 3223 is also designated LHS 1547. It is a white dwarf that is also color class G, a yellow degenerate. Credit: Aladin at SIMBAD.{{tlx|free media}}]]
EG 5 is a yellow degenerate.&lt;ref name=&quot;Greenstein&quot;&gt;{{cite journal
|author=Jesse L. Greenstein
|title=Photometry of a Pleiades candidate and composite white dwarfs
|journal=The Astronomical Journal
|date=September 1974
|volume=79
|issue=9
|pages=964-6
|url=
|arxiv=
|bibcode=1974AJ.....79..964G
|doi=10.1086/111638
|pmid=
|accessdate=2012-07-18 }}&lt;/ref&gt; EG 5 is another designation for Van Maanen's star.&lt;ref name=&quot;Strasbourg&quot;&gt;{{cite book
|author=Strasbourg astronomical Data Center
|title=NAME VAN MAANEN STAR -- White Dwarf
|publisher=Centre de Données astronomiques de Strasbourg
|location=Strasbourg, France
|date=July 19, 2012
|url=http://simbad.u-strasbg.fr/simbad/sim-basic?Ident=EG+5&amp;submit=SIMBAD+search
|accessdate=2012-07-18 }}&lt;/ref&gt;

'''Van Maanen's star''' ('''van Maanen 2''') is a [[w:white dwarf|white dwarf]] [[w:star|star]]. Out of the white dwarfs known, it is the third closest to the Sun, after [[w:Sirius B|Sirius B]] and [[w:Procyon B|Procyon B]], in that order, and the closest known solitary white dwarf.&lt;ref name=&quot;Henry&quot;&gt;{{cite book
| date=2008-01-01
| url=http://www.chara.gsu.edu/~thenry/RECONS/TOP100.posted.htm
| title=The One Hundred Nearest Star Systems
| publisher=RECONS
| accessdate=2008-12-08
}}&lt;/ref&gt;&lt;ref name=&quot;Holberg&quot;&gt;{{cite journal
| last1=Holberg
| first1=J. B.
| last2=Oswalt
| first2=Terry D.
| last3=Sion
| first3=E. M.
| title=A Determination of the Local Density of White Dwarf Stars
| journal=The Astrophysical Journal
| year=2002
| month=May
| volume=571
| issue=1
| pages=512–518
| doi=10.1086/339842
| bibcode=2002ApJ...571..512H
|arxiv = astro-ph/0102120
}}&lt;/ref&gt;

The optical negative at right was taken earlier than the current coordinates for Van Maanen's star, which are at the center of the negative.

Van Maanen's star has a radius of 9,000 ± 1,400 km.&lt;ref name=&quot;Gatewood&quot;&gt;{{cite journal
| last1=Gatewood
| first1=G.
| last2=Russell
| first2=J.
| title=Astrometric determination of the gravitational redshift of van Maanen 2 (EG 5)
| journal=Astronomical Journal
| year=1974
| month=July
| volume=79
| pages=815–818
| doi=10.1086/111613
| bibcode=1974AJ.....79..815G
}}&lt;/ref&gt; It's effective surface temperature is 6,220 ± 240 K.&lt;ref name=&quot;Sion&quot;&gt;{{cite journal
| title=The White Dwarfs Within 20 Parsecs of the Sun: Kinematics and Statistics
| author=Edward M. Sion
| last2=Holberg
| first2=J. B.
| last3=Oswalt
| first3=Terry D.
| last4=McCook
| first4=George P.
| last5=Wasatonic
| first5=Richard
| journal=The Astronomical Journal
| volume=138
| issue=6
| pages=1681–1689
| month=December
| year=2009
| doi=10.1088/0004-6256/138/6/1681
| bibcode=2009AJ....138.1681S
}}&lt;/ref&gt;

Degenerate stars are white dwarfs of spectral luminosity class VII.

Some yellow degenerate stars are of white dwarf spectral type DC (which show no detectable lines) mostly below T&lt;sub&gt;eff&lt;/sub&gt; &lt; 10,000 K.&lt;ref name=&quot;Greenstein&quot;/&gt;

At left is an Hertzsprung-Russell diagram which shows that luminosity class VII has color class G stars within.

At lower right is a close to true color visual image of GJ 3223, a yellow degenerate white dwarf.&lt;ref name=&quot;Greenstein&quot;/&gt; It is similar to other luminosity class VII yellow degenerates LHS 3369 and LHS 3399. Each is color class G, often written &quot;g&quot;&lt;ref name=&quot;Greenstein&quot;/&gt; when referring to white dwarfs.
{{clear}}

==Yellow subdwarfs==

Yellow subdwarfs are in luminosity class VI. &quot;[Y]ellow high-velocity subdwarfs are easily confused with white dwarfs in a proper-motion selection.&quot;&lt;ref name=&quot;Greenstein&quot;/&gt;

HD 64090 is a color class G0 subdwarf.

==Yellow main sequence stars==
[[Image:HD 86226 G2V.jpeg|thumb|right|250px|HD 86226 is a spectral type G2V yellow main sequence star. Credit: Aladin at SIMBAD.{{tlx|free media}}]]
The closest G2V yellow main sequence star is the Sun described above.

At right is a visual image in close to true color of the main sequence single star HD 86226. It has a parallax of 22.20 mas, but is not an X-ray source. A substellar companion HD 86226b has been detected.
{{clear}}

==Yellow subgiants==
[[Image:V972 Scorpii.jpeg|thumb|right|250px|V972 Scorpii is a variable star of the [[w:Delta Scuti variable|delta Scuti]] type. Spectral type is G2IV. Credit: Aladin at SIMBAD.{{tlx|free media}}]]
A '''subgiant star''' is a [[w:star|star]] that is slightly brighter than a normal [[w:main sequence|main-sequence]] (dwarf) star of the same [[w:stellar classification|spectral class]], but not as bright as true [[w:giant star|giant star]]s. Although certain subgiants appear to be simply unusually bright metal-rich hydrogen-fusing stars (in the same way [[w:subdwarf|subdwarf]]s are unusually dim metal-poor hydrogen-fusing stars), they are generally believed to be stars that are ceasing or have already ceased [[w:nuclear fusion|fusing]] [[w:hydrogen|hydrogen]] in their cores.

Many subgiants are rich in metals, and commonly host orbiting planets.

At right is a visual image in close to true color of V972 Scorpii, which is a variable star of the delta Sct type. It has spectral type G2IV and is a star in a cluster. The system includes components CCDM J16234-2622 A and CCDM J16234-2622 B. Component A is a dwarf star in a double star system with component B. Component A is apparently V972 Scuti.
{{clear}}

==Yellow giants==
[[Image:Alpha Microscopii.jpeg|thumb|right|250px|Alpha Microscopii is a spectral type G7III yellow giant star in a double system. Credit: Aladin at SIMBAD.{{tlx|free media}}]]
Alpha Microscopii is a spectral type G7III yellow giant star in a double system.

This star has an optical [[w:double star|visual companion]], CCDM J20500-3347B, of [[w:apparent visual magnitude|apparent visual magnitude]] 10.0 approximately 20.4 [[w:arcsecond|arcsecond]]s away at a [[w:position angle|position angle]] of 166°. It has no physical connection to the star described above.&lt;ref name=&quot;kaler&quot;&gt;[http://www.astro.uiuc.edu/~kaler/sow/alphamic.html Alpha Mic], Jim Kaler, ''Stars''. Accessed on line September 4, 2008.&lt;/ref&gt;
{{clear}}

==Barium stars==
{{main|Stars/Bariums}}
'''Barium stars''' are spectral class G to K giants, whose spectra indicate an overabundance of s-process elements by the presence of singly ionized barium, Ba II, at λ 455.4 nm. Barium stars also show enhanced spectral features of carbon, the bands of the molecules CH, CN and C&lt;sub&gt;2&lt;/sub&gt;.

Observational studies of their [[w:radial velocity|radial velocity]] suggested that all barium stars are [[w:binary stars|binary stars]]&lt;ref name=&quot;McClure&quot;&gt;McClure et al., Astrophysical Journal Letters, vol. 238, L35-L38, May 1980&lt;/ref&gt;&lt;ref&gt;McClure, R.D. &amp; Woodsworth, A.W. Astrophysical Journal, vol. 352, pp. 709–723, April 1990.&lt;/ref&gt;&lt;ref name=&quot;Jorissen&quot;&gt;Jorissen, A. &amp; Mayor, M. Astronomy &amp; Astrophysics, vol. 198, pp. 187–199, June 1988&lt;/ref&gt; Observations in the ultraviolet using the [[w:International Ultraviolet Explorer|International Ultraviolet Explorer]] detected [[w:white dwarfs|white dwarfs]] in some barium star systems.

Barium stars are believed to be the result of [[w:mass transfer|mass transfer]] in a binary star system. The mass transfer occurred when the presently-observed giant star was on the [[w:main sequence|main sequence]]. Its companion, the donor star, was a [[w:carbon star|carbon star]] on the [[w:asymptotic giant branch|asymptotic giant branch]] (AGB), and had produced carbon and s-process elements in its interior. These nuclear fusion products were mixed by [[w:convection|convection]] to its surface. Some of that matter &quot;polluted&quot; the surface layers of the main sequence star as the donor star lost mass at the end of its AGB evolution, and it subsequently evolved to become a white dwarf. We are observing these systems an indeterminate amount of time after the mass transfer event, when the donor star has long been a white dwarf, and the &quot;polluted&quot; recipient star has evolved to become a [[w:red giant|red giant]].&lt;ref name=&quot;McClure1985&quot;&gt;McClure, R. Journal of the Royals Astronomical Society of Canada, vol 79, pp. 277–293, Dec. 1985&lt;/ref&gt;&lt;ref&gt;Boffin, H. M. J. &amp; Jorissen, A., Astronomy &amp; Astrophysics, vol. 205, pp. 155–163, October 1988&lt;/ref&gt;

Barium stars exhibit carbon and s-process elements at their surfaces suggesting surface fusion possible during mass transfer or without it.

The mass transfer hypothesis predicts that there should be main sequence stars with barium star spectral peculiarities. At least one such star, HR 107, is known.&lt;ref name=&quot;Tomkin&quot;&gt;Tomkin, J., Lambert, D.L., Edvardsson, B., Gustafsson, B., &amp; Nissen, P.E., Astronomy &amp; Astrophysics, vol 219, pp. L15-L18, July 1989&lt;/ref&gt;

Prototypical barium stars include [[w:zeta Capricorni|zeta Capricorni]], HR 774, and HR 4474.

==Yellow supergiants==
[[Image:V781 Cas by SDSS.png|thumb|right|250px|V781 Cas was imaged by SDSS. Credit: SDSS.{{tlx|free media}}]]
A '''yellow supergiant (YSG)''' is a [[w:supergiant|supergiant]] star of [[w:spectral type|spectral type]] F or G.&lt;ref name=&quot;Chiosi&quot;&gt;{{cite journal
|title=The evolution of massive stars with mass loss
|author=Cesare Chiosi and Andre Maeder
|journal=Annual review of astronomy and astrophysics
|volume=24 1986
|pages=329&amp;ndash;75.
|bibcode=1986ARA&amp;A..24..329C
|doi=10.1146/annurev.aa.24.090186.001553 }}.&lt;/ref&gt; These stars usually have masses between 15 and 20 solar masses. These stars, like any other supergiant, are older and swing between blue and red phases depending on the chemical elements they consume in their cores. Until now it had been thought that few supergiants spend a long time in the transitional yellow phase. These systems may be the progenitors of rare supernovae linked to yellow supergiants. Only [a] few such supernovae have been detected - most supergiants go supernova when at the blue (or hot) phase or red (or cool) phase.
{{clear}}

==DY Persei variables==
[[Image:DY Persei.jpg|thumb|right|250px|DY Persei is shown in optical light. Credit: [[c:user:Dritter wiki|David Ritter]].{{tlx|free media}}]]
[[Image:DY Persei.png|thumb|left|250px|Light curve of DY Persei from 2014 to 2017 was created using the AAVSO light curve generator tool. Credit: [[c:user:Lithopsian|Lithopsian]].{{tlx|free media}}]]
DY Persei variables are a subclass of R Coronae Borealis variables. They are carbon-rich [[w:Asymptotic giant branch|asymptotic giant branch]] stars that exhibit [[w:Variable star#Pulsating variable stars|pulsational variability]] of AGB stars and [[w:irregular variable|irregular variability]] of RCB stars.

The star DY Persei is the prototype of this tiny class of variable stars.

DY Persei in the [[w:Perseus (constellation)|Perseus]] constellation pulsates like [[w:Variable star#Long period and semiregular variables|red variable]]s, ... [and fades] from sight like R Coronae Borealis variables.
{{clear}}

==R Coronae Borealis variable==
[[Image:R CrB.png|thumb|right|250px|The graph is of an [[w:AAVSO|AAVSO]] light curve of fadings by [[w:R Coronae Borealis|R Coronae Borealis]], the prototype star. Credit: [[w:User:Jimstars|Jimstars]].{{tlx|fairuse}}]]
An '''R Coronae Borealis variable''' (abbreviated '''RCB''') is an [[w:eruptive variable|eruptive variable]] star that varies in [[w:luminosity|luminosity]] in two modes, one low amplitude pulsation (a few tenths of a magnitude), and one irregular unpredictably sudden fading by 1 to 9 magnitudes.

The prototype star [is] [[w:R Coronae Borealis|R Coronae Borealis]] ... [O]nly about 100 RCB variables have been identified,&lt;ref name=&quot;ASAS&quot;&gt;{{cite journal
|eprint=1211.2475v2
|author1=Tisserand|author2=Clayton|author3=Welch|author4=Pilecki|author5=Wyrzykowski|author6=Kilkenny
|title=The ongoing pursuit of R Coronae Borealis stars: ASAS-3 survey strikes again
|class=astro-ph.SR 2012
|url=https://books.google.com/books?isbn=3527655204 }}&lt;/ref&gt; making this class a very rare kind of star.

The fading is caused by condensation of carbon to soot, making the star fade in visible light while measurements in infrared light exhibit no real luminosity decrease. R Coronae Borealis variables are typically supergiant stars in the [[w:stellar classification|spectral classes]] F and G (by convention called &quot;yellow&quot;), with typical C&lt;sub&gt;2&lt;/sub&gt; and [[w:Cyanide|CN]] molecular bands, characteristic of yellow supergiants. RCB star atmospheres do however lack hydrogen by an abundance of 1 part per 1,000 down to 1 part per 1,000,000 relative to helium and other chemical elements, while the [[w:universe|universal]] abundance of hydrogen is about 3 to 1 relative to helium.

There is a considerable variation in spectrum between various RCB specimens. Most of the stars with known spectrum are either [[w:stellar classification|F to G class]] (&quot;yellow&quot;) supergiants, or a comparatively cooler C-R type [[w:carbon star|carbon star]] supergiant. Three of the stars are however of the &quot;blue&quot; B type, for example VZ Sagittarii, and one is a &quot;red&quot; giant star, V482 Cygni of type M5III. Four stars are unusually and inexplicably poor in iron [[w:fraunhofer line|absorption lines]] in the spectrum.&lt;ref name=Clayton&gt;{{cite journal
|author=Geoffrey C. Clayton
|title=The R Coronae Borealis Stars
|date=19986
|journal=Publications of the Astronomical Society of the Pacific
|volume=198
|issue=71
|url=https://iopscience.iop.org/article/10.1086/133715
|doi=10.1086/133715
|accessdate=26 July 2019 }}&lt;/ref&gt; The constant features are prominent Carbon lines, strong atmospheric Hydrogen deficiencies, and obviously the intermittent fadings.
{{clear}}

==Yellow hypergiants==
[[Image:Rho Cassiopeiae1.jpeg|thumb|right|250px|Rho Cassiopeiae is a semi-regular pulsating star of spectral class G2Ia0e. Credit: Aladin at SIMBAD.{{tlx|fairuse}}]]
&quot;''ρ'' Cas, HR 8752 and IRC+10420, three well-studied yellow hypergiants, are situated at or close to the red border of the [yellow evolutionary] void.&quot;&lt;ref name=&quot;Nieuwenhuijzen&quot;/&gt;

Generally speaking, a '''yellow hypergiant''' is a massive star with an extended atmosphere, which can be classified as spectral class from late A to K, with a mass of as much as 20-50 [[w:solar masses|solar masses]]. Yellow [[w:hypergiant|hypergiant]]s, such as [[w:Rho Cassiopeiae|Rho Cassiopeiae]] in the constellation [[w:Cassiopeia (constellation)|Cassiopeia]], have been observed to experience periodic eruptions, resulting in periodic or continuous dimming of the star, respectively. Yellow hypergiants appear to be extremely rare in the universe. Due to their extremely rapid rate of consumption of nuclear fuel, yellow hypergiants generally only remain on the [[w:main sequence|main sequence]] for a few million years before destroying themselves in a massive [[w:supernova|supernova]] or [[w:hypernova|hypernova]]. Yellow hypergiants are post-[[w:red supergiants|red supergiants]], rapidly evolving toward the [[w:blue supergiant|blue supergiant]] phase.

According to the current physical models of stars, a yellow hypergiant should possess a convective core surrounded by a radiative zone, as opposed to a sun-sized star, which consists of a radiative core surrounded by a convective zone (Seeds, 2005). Due to the extremely high pressures which exist at the core of a yellow hypergiant, portions of the core or perhaps the entire core may be composed of degenerate matter.

These stars have powerful magnetic fields.
{{clear}}

==Yellow evolutionary void==

G is host to the &quot;Yellow Evolutionary Void&quot;.&lt;ref name=&quot;Nieuwenhuijzen&quot;&gt;{{cite journal
|author=H. Nieuwenhuijzen &amp; C. de Jager
|title=Checking the yellow evolutionary void. Three evolutionary critical Hypergiants: HD 33579, HR 8752 &amp; IRC +10420
|journal=Astronomy and Astrophysics
|date=January 2000
|volume=353
|issue=1
|pages=163-76
|url=
|arxiv=
|bibcode=2000A&amp;A...353..163N
|doi=
|pmid=
|accessdate=2012-03-19 }}&lt;/ref&gt; Supergiant stars often swing between O or B (blue) and K or M (red). While they do this, they do not stay for long in the G classification as this is an extremely unstable place for a supergiant to be.

&quot;[T]he yellow evolutionary void ... is an area in the Hertzspung-Russell diagram where atmospheres of blueward evolving super- and hypergiants are moderately unstable ... For [such stars] (in hydrostatic equilibrium)
# a negative density gradient occurs,
# the sum of all accelerations, including wind, turbulence and pulsations, is zero or negative,
# the sonic point of the stellar wind is reached in or below photospheric levels, and
# Γ&lt;sub&gt;1&lt;/sub&gt; ≤ 4/3 indicating some level of dynamic instability in part of the atmosphere.&quot;&lt;ref name=&quot;Nieuwenhuijzen&quot;/&gt;

==Yellow galaxies==
[[Image:grav.lens1.arp.750pix.jpg|thumb|250px|This image shows a cluster of yellow galaxies near the middle of the photograph. Credit: STScl/NASA.{{tlx|free media}}]]
The image at right shows several blue, loop-shaped objects that are multiple images of the same galaxy, duplicated by the [[w:gravitational lens|gravitational lens]] effect of the cluster of yellow galaxies near the middle of the photograph. The lens is produced by the cluster's gravitational field that bends light to magnify and distort the image of a more distant object.
{{clear}}

==Hypotheses==
{{main|Hypotheses}}
# Each of the planets revolving around Sol can be seen in the yellow.

==See also==
{{div col|colwidth=20em}}
* [[Blue astronomy]]
* [[Cyan astronomy]]
* [[First yellow source in Aquila]]
* [[Gamma-ray astronomy]]
* [[Green astronomy]]
* [[Infrared astronomy]]
* [[Microwave astronomy]]
* [[Optical astronomy]]
* [[Orange astronomy]]
* [[Radar astronomy]]
* [[Radio astronomy]]
* [[Red astronomy]]
* [[Submillimeter astronomy]]
* [[Ultraviolet astronomy]]
* [[Violet astronomy]]
* [[Visual astronomy]]
* [[X-ray astronomy]]
* [[Yellow astronomy]]
{{Div col end}}

==References==
{{reflist|2}}

==Further reading==
* {{cite book |author=Eberhard Haug &amp; Werner Nakel|title=The elementary process of Bremsstrahlung |year= 2004 |page =''Scientific lecture notes in physics, vol. 73'' |publisher=World Scientific |location=River Edge NJ |isbn=9812385789 |url=http://books.google.com/books?hl=en&amp;id=v4FMtIwTri8C&amp;dq=bremsstrahlung+haug&amp;printsec=frontcover&amp;source=web&amp;ots=THjay1eeFA&amp;sig=aHe-xMFwT8jxhpAGJHDnxKC6Jjc#PPA29,M1 }}

==External links==
* [http://www.iau.org/ International Astronomical Union]
* [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED]
* [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center]
* [http://www.ncbi.nlm.nih.gov/sites/gquery NCBI All Databases Search]
* [http://www.osti.gov/ Office of Scientific &amp; Technical Information]
* [http://www.ncbi.nlm.nih.gov/pccompound PubChem Public Chemical Database]
* [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System]
* [http://www.scirus.com/srsapp/advanced/index.jsp?q1= Scirus for scientific information only advanced search]
* [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer]
* [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database]
* [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA]
* [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter]

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      <text bytes="5056" sha1="tcwi47k7z9eaua34aeth259z0ekv7js" xml:space="preserve">This is the beginning of &quot;The Department of Folk Music&quot; in &quot;The School of Creativity (just a stub for now). [[User:Ray Calvin Baker|Ray Calvin Baker]] ([[User talk:Ray Calvin Baker|talk]]) 00:30, 4 October 2012 (UTC)

Many senior citizens remember folk songs they learned in their youth. They like to sing them, read stories about their origins and history, and some are even creative and bold enough to add verses to old folk songs, or to create entirely new songs to share with their friends.

&quot;Sing-along&quot; activities can be greatly facilitated when song lyrics and arrangements for simple but suitable instrumental accompaniments can be made easily available. Wikimedia Commons seems like a convenient place to store such public-domain material. Projection of suitable graphical displays can be usefully employed by groups of any size, from simple equipment -- a laptop computer connected to a projector and to the internet.

This Department is intended to support all of these purposes, and to encourage wider participation and use of the Wikiversity. It is my hope that this Department can be expanded to support the &quot;sing-along&quot; activities of the Senior Center of Caroline County (Maryland) In the town of Denton. I expect that the support and participation of my friends there can productively guide the expansion of this Department. [[User:Ray Calvin Baker|Ray Calvin Baker]] ([[User talk:Ray Calvin Baker|talk]]) 00:30, 4 October 2012 (UTC)

==She'll Be Comin' 'Round the Mountain==

This is one of the songs we enjoy singing together at the Caroline County Senior Center. We have not yet performed it correctly, with the silly motions, but we have been having fun trying.

(&quot;Toot! Toot!&quot; -- pull the cord on a riverboat's steam whistle)

She'll be comin' 'round the mountain, when she comes: &quot;toot! toot!&quot;&lt;br&gt; 
She'll be comin' 'round the mountain, when she comes: &quot;toot! toot!&quot;&lt;br&gt; 
She'll be comin' 'round the mountain,&lt;br&gt;
She'll be comin' 'round the mountain,&lt;br&gt;
She'll be comin' 'round the mountain, when she comes: &quot;toot! toot!&quot; 

(&quot;Whoa, back!&quot; -- pull on the reins of the six white horses)

She'll be drivin' six white horses when she comes: &quot;Whoa, back! toot! toot!&quot;&lt;br&gt;
She'll be drivin' six white horses when she comes: &quot;Whoa, back! toot! toot!&quot;&lt;br&gt;
She'll be drivin' six white horses,&lt;br&gt;
She'll be drivin' six white horses,&lt;br&gt;
She'll be drivin' six white horses when she comes: &quot;Whoa, back! toot! toot!&quot;

(&quot;Scratch, scratch!&quot; -- old red flannel underwear itches!)

She'll be wearin' old red flannels when she comes: &quot;Scratch, scratch! Whoa, back! toot! toot!&quot;&lt;br&gt;
She'll be wearin' old red flannels when she comes: &quot;Scratch, scratch! Whoa, back! toot! toot!&quot;&lt;br&gt;
She'll be wearin' old red flannels,&lt;br&gt;
She'll be wearin' old red flannels,&lt;br&gt;
She'll be wearin' old red flannels when she comes: &quot;Scratch, scratch! Whoa, back! toot! toot!&quot;

(&quot;Whack, whack!&quot; -- chop off the head of the old red rooster.)

Oh, we'll kill the old red rooster when she comes: &quot;Whack, whack! Scratch, scratch, Whoa, back! toot! toot!&quot;&lt;br&gt;
Oh, we'll kill the old red rooster when she comes: &quot;Whack, whack! Scratch, scratch, Whoa, back! toot! toot!&quot;&lt;br&gt;
Oh, we'll kill the old red rooster,&lt;br&gt;
Oh, we'll kill the old red rooster,&lt;br&gt;
Oh, we'll kill the old red rooster when she comes: &quot;Whack, whack! Scratch, scratch, Whoa, back! toot! toot!&quot;

(&quot;Yum! Yum!&quot; -- rub your tummy)

Oh, we'll all have chicken an' dumplin's when she comes: &quot;Yum! Yum! Whack, whack! Scratch, scratch, Whoa, back! toot! toot!&quot;&lt;br&gt;
Oh, we'll all have chicken an' dumplin's when she comes: &quot;Yum! Yum! Whack, whack! Scratch, scratch, Whoa, back! toot! toot!&quot;&lt;br&gt;
Oh, we'll all have chicken an' dumplin's,&lt;br&gt;
Oh, we'll all have chicken an' dumplin's,&lt;br&gt;
Oh, we'll all have chicken an' dumplin's when she comes: &quot;Yum! Yum! Whack, whack! Scratch, scratch, Whoa, back! toot! toot!&quot;&lt;br&gt;

(&quot;Hi, Babe!&quot; -- wave, &quot;hello!&quot;)

Oh, we'll all come out to meet her, when she comes: &quot;Hi, Babe!, Yum! Yum! Whack, whack! Scratch, scratch, Whoa, back, toot! toot!&lt;br&gt;
Oh, we'll all come out to meet her, when she comes: &quot;Hi, Babe!, Yum! Yum! Whack, whack! Scratch, scratch, Whoa, back, toot! toot!&lt;br&gt;
Oh, we'll all come out to meet her,&lt;br&gt;
Oh, we'll all come out to meet her,&lt;br&gt;
Oh, we'll all come out to meet her, when she comes: &quot;Hi, Babe!, Yum! Yum! Whack, whack! Scratch, scratch, Whoa, back, toot! toot!

This has not yet been put into a form suitable for Wikimedia Commons. Content first, then nice formatting. [[User:Ray Calvin Baker|Ray Calvin Baker]] ([[User talk:Ray Calvin Baker|talk]]) 00:56, 4 October 2012 (UTC)&lt;br&gt;
I finished the song. [[User:Ray Calvin Baker|Ray Calvin Baker]] ([[User talk:Ray Calvin Baker|talk]]) 02:01, 4 October 2012 (UTC)

==Back to the School of Creativity==

Here is a link to take you directly back to the School of Creativity, in case you would like to explore other Departments there. [[School:Creativity]]

[[User:Ray Calvin Baker|Ray Calvin Baker]] ([[User talk:Ray Calvin Baker|talk]]) 21:15, 5 October 2012 (UTC)

[[Category:Music genres and styles]]</text>
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    <title>Understanding Arithmetic Circuits</title>
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      <contributor>
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        <id>21186</id>
      </contributor>
      <comment>/* Adder */</comment>
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== Adder ==

* Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]]  )
 
{| class=&quot;wikitable&quot;
|-
!  Adder type      !! Overview !! Analysis !! VHDL Level Design  !! CMOS Level Design  
|-
| '''1. Ripple Carry Adder'''
|| [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]||
|| [[Media:Adder.rca.20140313.pdf|pdf]]
|| [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]]
|-
| '''2. Carry Lookahead Adder'''
|| [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260918.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260918.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] ||
|| [[Media:Adder.cla.20140313.pdf|pdf]]||
|-
| '''3. Carry Save Adder''' 
|| [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]||
|| ||
|-
|| '''4. Carry Select Adder''' 
|| [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]||
|| || 
|-
|| '''5. Carry Skip Adder'''
|| [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]||
|| 
|| [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]]
|- 
|| '''6. Carry Chain Adder'''
|| [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]||
|| [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]],  [[Media:Adder.cca.20140313.pdf|pdf]]
|| [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]]
|- 
|| '''7. Kogge-Stone Adder'''
|| [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]||
|| [[Media:Adder.ksa.20140409.pdf|pdf]]||
|-
|| '''8. Prefix Adder'''
|| [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]||
|| || 
|-
|| '''9.1 Variable Block Adder'''
|| [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]||
|| || 
|-
|| '''9.2 Multi-Level Variable Block Adder'''
|| [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]||
|| || 
|}
&lt;/br&gt;
 
=== Adder Architectures Suitable for FPGA === 
* FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]])
* FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]])
* FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]])
* FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]])
* Carry-Skip Adder
&lt;/br&gt;

== Barrel Shifter ==
* Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]])
&lt;/br&gt;

'''Mux Based Barrel Shifter'''
* Analysis  ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) 
* Implementation 
&lt;/br&gt;

== Multiplier == 
=== Array Multipliers ===
* Analysis  ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]])
&lt;/br&gt;

=== Tree Mulltipliers ===
* Lattice Multiplication  ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]])
* Wallace Tree  ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]])
* Dadda Tree  ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]])
&lt;/br&gt;

=== Booth Multipliers ===
* [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]]
* Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]])
&lt;/br&gt;

== Divider == 
* Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])&lt;/br&gt;

&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

[[Category:Digital Circuit Design]]
[[Category:FPGA]]</text>
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    <title>Talk:Islam/Sunni Islam</title>
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      <text bytes="925" sha1="jrihjyg6t27m2vmnirl9lell4jnsozz" xml:space="preserve">Note: That everything under the Background research will be copied excatly from the source, sources may be listed. --&lt;span style=&quot;text-shadow:-3px 2 red,0 1px lightred,1px 0 red,0 -1px red;&quot;&gt;[[User:Goldenburg111|&lt;b style=&quot;color:blue&quot;&gt;Aaqib&lt;/b&gt;]]&lt;/span&gt; {{font|face=&quot;Comic Sans MS&quot;|size=x-small|[[User talk:Goldenburg111|&lt;b style=&quot;color:black&quot;&gt;talk&lt;/b&gt;]]}} 12:24, 25 October 2013 (UTC)

== Background research ==
'''Note:''' All material presented under the '''“Background Research”''' section shall be reproduced verbatim from the respective original sources, without alteration, modification, or omission. Appropriate source citations and references may be provided to ensure transparency, accuracy, and facilitate independent verification of the information presented. [[User:Samargul555|Samargul555]] ([[User talk:Samargul555|discuss]] • [[Special:Contributions/Samargul555|contribs]]) 12:16, 17 September 2026 (UTC)</text>
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  <page>
    <title>Complex analysis in plain view</title>
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      <contributor>
        <username>Young1lim</username>
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      <comment>/* Geometric Series Examples */</comment>
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      <text bytes="5296" sha1="eb0wz8yxrk841x4pangkmbqxnoxijvb" xml:space="preserve">Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers &lt;math&gt;x+iy&lt;/math&gt;, where &lt;math&gt;i=\sqrt{-1}&lt;/math&gt;, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other &lt;math&gt;L&lt;/math&gt;-functions, modular forms, elliptic functions, etc. &lt;blockquote&gt;The shortest path between two truths in the real domain passes through the complex domain.  — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]&lt;/blockquote&gt;In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}}

==''' Complex Functions '''== 
* Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]])

* Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]])

* Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]])

'''Complex Function Note'''
: 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]])

: 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]])

: 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]])

==''' Complex Integrals '''== 
* Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]])

==''' Complex Series '''== 
* Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]])

==''' Residue Integrals '''==
* Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) 

==='''Residue Integrals Note'''===
* Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]])
* Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]])
* Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]])
* Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]])

=== Laurent Series and the z-Transform Example Note === 
* Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]])

====Geometric Series Examples====

* Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) 

* Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) 

* Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) 

* Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) 

* Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) 

* Permutations ([[Media:Laurent.6.Permutation.6A.20230711.pdf|A.pdf]], [[Media:Laurent.5.Permutation.6B.20251225.pdf|B.pdf]], [[Media:Laurent.5.Permutation.6C.20260917.pdf|C.pdf]], [[Media:Laurent.5.Permutation.6C.20240528.pdf|D.pdf]]) 

* Applications ([[Media:Laurent.5.Application.6B.20220723.pdf|A.pdf]]) 

* Double Pole Case

:- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) 

:- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]])

====The Case Examples====
* Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]])
* Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]])
* Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]])
* Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]])
* Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]])
* Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]])

==''' Conformal Mapping '''== 
* Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]])

go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

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    <title>Minimal negation operator</title>
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      <text bytes="18839" sha1="rhoh4t9s1g9jwx0gho7l2mf007973tq" xml:space="preserve">{{font|size=medium|&amp;#9758;}} This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

A '''minimal negation operator''' &lt;math&gt;(\nu)&lt;/math&gt; is a logical connective which says &amp;ldquo;just one false&amp;rdquo; of its logical arguments.&amp;nbsp; The first four cases are described below.

&lt;ol start=&quot;0&quot;&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If the list of arguments is empty, as expressed in the form &lt;math&gt;\nu(),&lt;/math&gt; then it cannot be true that exactly one of the arguments is false, so &lt;math&gt;\nu() = \mathrm{false}.&lt;/math&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; is the only argument then &lt;math&gt;\nu(p)&lt;/math&gt; says that &lt;math&gt;p&lt;/math&gt; is false, so &lt;math&gt;\nu(p)&lt;/math&gt; expresses the logical negation of the proposition &lt;math&gt;p.&lt;/math&gt;&amp;nbsp; Written in several different notations, we have the following equivalent expressions.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p) ~=~ \mathrm{not}(p) ~=~ \lnot p ~=~ \tilde{p} ~=~ p^{\prime}&lt;/math&gt;&lt;/p&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; and &lt;math&gt;q&lt;/math&gt; are the only two arguments then &lt;math&gt;\nu(p, q)&lt;/math&gt; says that exactly one of &lt;math&gt;p, q&lt;/math&gt; is false, so &lt;math&gt;\nu(p, q)&lt;/math&gt; says the same thing as &lt;math&gt;p \neq q.&lt;/math&gt;  Expressing &lt;math&gt;\nu(p, q)&lt;/math&gt; in terms of ands &lt;math&gt;(\cdot),&lt;/math&gt; ors &lt;math&gt;(\lor),&lt;/math&gt; and nots &lt;math&gt;(\tilde{~})&lt;/math&gt; gives the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p} \cdot q ~\lor~ p \cdot \tilde{q}&lt;/math&gt;&lt;/p&gt;

It is permissible to omit the dot &lt;math&gt;(\cdot)&lt;/math&gt; in contexts where it is understood, giving the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p}q \lor p\tilde{q}&lt;/math&gt;&lt;/p&gt;

The venn diagram for &lt;math&gt;\nu(p, q)&lt;/math&gt; is shown in Figure&amp;nbsp;1.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 1.}~~\nu(p, q)&lt;/math&gt;&lt;/p&gt;
|}
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
The venn diagram for &lt;math&gt;\nu(p, q, r)&lt;/math&gt; is shown in Figure&amp;nbsp;2.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 2.}~~\nu(p, q, r)&lt;/math&gt;&lt;/p&gt;
|}

The center cell is the region where all three arguments &lt;math&gt;p, q, r&lt;/math&gt; hold true, so &lt;math&gt;\nu(p, q, r)&lt;/math&gt; holds true in just the three neighboring cells.&amp;nbsp; In other words:

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q, r) ~=~ \tilde{p}qr \lor p\tilde{q}r \lor pq\tilde{r}&lt;/math&gt;&lt;/p&gt;

&lt;/li&gt;&lt;/ol&gt;

==Initial definition==

The '''minimal negation operator''' &lt;math&gt;\nu&lt;/math&gt; is a [[multigrade operator]] &lt;math&gt;(\nu_k)_{k \in \mathbb{N}}&lt;/math&gt; where each &lt;math&gt;\nu_k&lt;/math&gt; is a &lt;math&gt;k&lt;/math&gt;-ary [[boolean function]] defined by the rule that &lt;math&gt;\nu_k (x_1, \ldots , x_k) = 1&lt;/math&gt; if and only if exactly one of the arguments &lt;math&gt;x_j&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;

In contexts where the initial letter &lt;math&gt;\nu&lt;/math&gt; is understood, the minimal negation operators can be indicated by argument lists in parentheses.&amp;nbsp; In the following text a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, &lt;math&gt;\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} = \nu (x, y, z).&lt;/math&gt;

The first four members of this family of operators are shown below.&amp;nbsp; The third and fourth columns give paraphrases in two other notations, where tildes and primes, respectively, indicate logical negation.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(x)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x^\prime
\\[6pt]
\texttt{(x, y)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x^\prime y \lor x y^\prime
\\[6pt]
\texttt{(x, y, z)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x^\prime y z \lor x y^\prime z \lor x y z^\prime
\end{matrix}&lt;/math&gt;
|}

==Formal definition==

To express the general case of &lt;math&gt;\nu_k&lt;/math&gt; in terms of familiar operations, it helps to introduce an intermediary concept:

'''Definition.'''&amp;nbsp; Let the function &lt;math&gt;\lnot_j : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; be defined for each integer &lt;math&gt;j&lt;/math&gt; in the interval &lt;math&gt;[1, k]&lt;/math&gt; by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\lnot_j (x_1, \ldots, x_j, \ldots, x_k) ~=~ x_1 \land \ldots \land x_{j-1} \land \lnot x_j \land x_{j+1} \land \ldots \land x_k.&lt;/math&gt;
|}

Then &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; is defined by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\nu_k (x_1, \ldots, x_k) ~=~ \lnot_1 (x_1, \ldots, x_k) \lor \ldots \lor \lnot_j (x_1, \ldots, x_k) \lor \ldots \lor \lnot_k (x_1, \ldots, x_k).&lt;/math&gt;
|}

If we take the boolean product &lt;math&gt;x_1 \cdot \ldots \cdot x_k&lt;/math&gt; or the logical conjunction &lt;math&gt;x_1 \land \ldots \land x_k&lt;/math&gt; to indicate the point &lt;math&gt;x = (x_1, \ldots, x_k)&lt;/math&gt; in the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; then the minimal negation &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; indicates the set of points in &lt;math&gt;\mathbb{B}^k&lt;/math&gt; that differ from &lt;math&gt;x&lt;/math&gt; in exactly one coordinate.&amp;nbsp; This makes &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; a discrete functional analogue of a point-omitted neighborhood in ordinary real analysis, more exactly, a point-omitted distance-one neighborhood.&amp;nbsp; In this light, the minimal negation operator can be recognized as a differential construction, an observation that opens a very wide field.

The remainder of this discussion proceeds on the algebraic convention that the plus sign &lt;math&gt;(+)&lt;/math&gt; and the summation symbol &lt;math&gt;(\textstyle\sum)&lt;/math&gt; both refer to addition mod 2.&amp;nbsp; Unless otherwise noted, the boolean domain &lt;math&gt;\mathbb{B} = \{ 0, 1 \}&lt;/math&gt; is interpreted for logic in such a way that &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;&amp;nbsp; This has the following consequences:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;x + y&lt;/math&gt; is a function equivalent to the exclusive disjunction of &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y,&lt;/math&gt; while its fiber of 1 is the relation of inequality between &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;\textstyle\sum_{j=1}^k x_j&lt;/math&gt; maps the bit sequence &lt;math&gt;(x_1, \ldots, x_k)&lt;/math&gt; to its ''parity''.
|}

The following properties of the minimal negation operators &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; may be noted:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The function &lt;math&gt;\texttt{(x, y)}&lt;/math&gt; is the same as that associated with the operation &lt;math&gt;x + y&lt;/math&gt; and the relation &lt;math&gt;x \ne y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| In contrast, &lt;math&gt;\texttt{(x, y, z)}&lt;/math&gt; is not identical to &lt;math&gt;x + y + z.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| More generally, the function &lt;math&gt;\nu_k (x_1, \dots, x_k)&lt;/math&gt; for &lt;math&gt;k &gt; 2&lt;/math&gt; is not identical to the boolean sum &lt;math&gt;\textstyle\sum_{j=1}^k x_j.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The inclusive disjunctions indicated for the &lt;math&gt;\nu_k&lt;/math&gt; of more than one argument may be replaced with exclusive disjunctions without affecting the meaning since the terms in disjunction are already disjoint.
|}

==Truth tables==

Table&amp;nbsp;3 is a [[truth table]] for the sixteen boolean functions of type &lt;math&gt;f : \mathbb{B}^3 \to \mathbb{B}&lt;/math&gt; whose fibers of 1 are either the boundaries of points in &lt;math&gt;\mathbb{B}^3&lt;/math&gt; or the complements of those boundaries.

&lt;br&gt;

{| align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;8&quot; cellspacing=&quot;0&quot; style=&quot;text-align:center; width:70%&quot;
|+ &lt;math&gt;\text{Table 3.} ~~ \text{Logical Boundaries and Their Complements}&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &lt;math&gt;\mathcal{L}_1&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_2&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_3&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_4&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;p\colon&lt;/math&gt;
| &lt;math&gt;1~1~1~1~0~0~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;q\colon&lt;/math&gt;
| &lt;math&gt;1~1~0~0~1~1~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;r\colon&lt;/math&gt;
| &lt;math&gt;1~0~1~0~1~0~1~0&lt;/math&gt;
| &amp;nbsp;
|-
|
&lt;math&gt;\begin{matrix}
f_{104}
\\[4pt]
f_{148}
\\[4pt]
f_{146}
\\[4pt]
f_{97}
\\[4pt]
f_{134}
\\[4pt]
f_{73}
\\[4pt]
f_{41}
\\[4pt]
f_{22}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{01101000}
\\[4pt]
f_{10010100}
\\[4pt]
f_{10010010}
\\[4pt]
f_{01100001}
\\[4pt]
f_{10000110}
\\[4pt]
f_{01001001}
\\[4pt]
f_{00101001}
\\[4pt]
f_{00010110}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
0~1~1~0~1~0~0~0
\\[4pt]
1~0~0~1~0~1~0~0
\\[4pt]
1~0~0~1~0~0~1~0
\\[4pt]
0~1~1~0~0~0~0~1
\\[4pt]
1~0~0~0~0~1~1~0
\\[4pt]
0~1~0~0~1~0~0~1
\\[4pt]
0~0~1~0~1~0~0~1
\\[4pt]
0~0~0~1~0~1~1~0
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(}~p~\texttt{,}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,}~q~\texttt{,}(r\texttt{))}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),(}r\texttt{))}
\end{matrix}&lt;/math&gt;
|-
|
&lt;math&gt;\begin{matrix}
f_{233}
\\[4pt]
f_{214}
\\[4pt]
f_{182}
\\[4pt]
f_{121}
\\[4pt]
f_{158}
\\[4pt]
f_{109}
\\[4pt]
f_{107}
\\[4pt]
f_{151}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{11101001}
\\[4pt]
f_{11010110}
\\[4pt]
f_{10110110}
\\[4pt]
f_{01111001}
\\[4pt]
f_{10011110}
\\[4pt]
f_{01101101}
\\[4pt]
f_{01101011}
\\[4pt]
f_{10010111}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
1~1~1~0~1~0~0~1
\\[4pt]
1~1~0~1~0~1~1~0
\\[4pt]
1~0~1~1~0~1~1~0
\\[4pt]
0~1~1~1~1~0~0~1
\\[4pt]
1~0~0~1~1~1~1~0
\\[4pt]
0~1~1~0~1~1~0~1
\\[4pt]
0~1~1~0~1~0~1~1
\\[4pt]
1~0~0~1~0~1~1~1
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(((}p\texttt{),(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,}~r~\texttt{))}
\end{matrix}&lt;/math&gt;
|}

&lt;br&gt;

==Charts and graphs==

This Section focuses on visual representations of minimal negation operators.  A few bits of terminology are useful in describing the pictures, but the formal details are tedious reading, and may be familiar to many readers, so the full definitions of the terms marked in ''italics'' are relegated to a Glossary at the end of the article.

Two ways of visualizing the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; of &lt;math&gt;2^k&lt;/math&gt; points are the ''hypercube'' picture and the ''venn diagram'' picture.  The hypercube picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique point of the &lt;math&gt;k&lt;/math&gt;-dimensional hypercube.  The venn diagram picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique &amp;ldquo;cell&amp;rdquo; of the venn diagram on &lt;math&gt;k&lt;/math&gt; &amp;ldquo;circles&amp;rdquo;.

In addition, each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' &lt;math&gt;[|s|]&lt;/math&gt; of a ''singular proposition'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; and thus it is the unique point where a ''singular conjunction'' of &lt;math&gt;k&lt;/math&gt; ''literals'' is &lt;math&gt;1.&lt;/math&gt;

For example, consider two cases at opposite vertices of the cube:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(1, 1, \ldots , 1, 1)&lt;/math&gt; with all 1's as coordinates is the point where the conjunction of all posited variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;x_1 ~ x_2 ~\ldots~ x_{n-1} ~ x_n ~=~ 1.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(0, 0, \ldots , 0, 0)&lt;/math&gt; with all 0's as coordinates is the point where the conjunction of all negated variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;\texttt{(} x_1 \texttt{)(} x_2 \texttt{)} \ldots \texttt{(} x_{n-1} \texttt{)(} x_n \texttt{)} ~=~ 1.&lt;/math&gt;
|}

To pass from these limiting examples to the general case, observe that a singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be given canonical expression as a conjunction of literals, &lt;math&gt;s = e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;.  Then the proposition &lt;math&gt;\nu (e_1, e_2, \ldots, e_{k-1}, e_k)&lt;/math&gt; is &lt;math&gt;1&lt;/math&gt; on the points adjacent to the point where &lt;math&gt;s&lt;/math&gt; is &lt;math&gt;1,&lt;/math&gt; and 0 everywhere else on the cube.

For example, consider the case where &lt;math&gt;k = 3.&lt;/math&gt;  Then the minimal negation operation &lt;math&gt;\nu (p, q, r)&lt;/math&gt; &amp;mdash; written more simply as &lt;math&gt;\texttt{(p, q, r)}&lt;/math&gt; &amp;mdash; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 4.}~~\texttt{(p, q, r)}&lt;/math&gt;&lt;/p&gt;
|}

For a contrasting example, the boolean function expressed by the form &lt;math&gt;\texttt{((p),(q),(r))}&lt;/math&gt; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram ((P),(Q),(R)).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 5.}~~\texttt{((p),(q),(r))}&lt;/math&gt;&lt;/p&gt;
|}

==Glossary of basic terms==

; Boolean domain
: A ''[[boolean domain]]'' &lt;math&gt;\mathbb{B}&lt;/math&gt; is a generic 2-element set, for example, &lt;math&gt;\mathbb{B} = \{ 0, 1 \},&lt;/math&gt; whose elements are interpreted as logical values, usually but not invariably with &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;

; Boolean variable
: A ''boolean variable'' &lt;math&gt;x&lt;/math&gt; is a variable that takes its value from a boolean domain, as &lt;math&gt;x \in \mathbb{B}.&lt;/math&gt;

; Proposition
: In situations where boolean values are interpreted as logical values, a [[boolean-valued function]] &lt;math&gt;f : X \to \mathbb{B}&lt;/math&gt; or a [[boolean function]] &lt;math&gt;g : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is frequently called a ''proposition''.

; Basis element, Coordinate projection
: Given a sequence of &lt;math&gt;k&lt;/math&gt; boolean variables, &lt;math&gt;x_1, \ldots, x_k,&lt;/math&gt; each variable &lt;math&gt;x_j&lt;/math&gt; may be treated either as a ''basis element'' of the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; or as a ''coordinate projection'' &lt;math&gt;x_j : \mathbb{B}^k \to \mathbb{B}.&lt;/math&gt;

; Basic proposition
: This means that the set of objects &lt;math&gt;\{ x_j : 1 \le j \le k \}&lt;/math&gt; is a set of boolean functions &lt;math&gt;\{ x_j : \mathbb{B}^k \to \mathbb{B} \}&lt;/math&gt; subject to logical interpretation as a set of ''basic propositions'' that collectively generate the complete set of &lt;math&gt;2^{2^k}&lt;/math&gt; propositions over &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Literal
: A ''literal'' is one of the &lt;math&gt;2k&lt;/math&gt; propositions &lt;math&gt;x_1, \ldots, x_k, \texttt{(} x_1 \texttt{)}, \ldots, \texttt{(} x_k \texttt{)},&lt;/math&gt; in other words, either a ''posited'' basic proposition &lt;math&gt;x_j&lt;/math&gt; or a ''negated'' basic proposition &lt;math&gt;\texttt{(} x_j \texttt{)},&lt;/math&gt; for some &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

; Fiber
: In mathematics generally, the ''[[fiber (mathematics)|fiber]]'' of a point &lt;math&gt;y \in Y&lt;/math&gt; under a function &lt;math&gt;f : X \to Y&lt;/math&gt; is defined as the inverse image &lt;math&gt;f^{-1}(y) \subseteq X.&lt;/math&gt;

: In the case of a boolean function &lt;math&gt;f : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; there are just two fibers:
: The fiber of &lt;math&gt;0&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(0),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;
: The fiber of &lt;math&gt;1&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(1),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;1.&lt;/math&gt;

; Fiber of truth
: When &lt;math&gt;1&lt;/math&gt; is interpreted as the logical value &lt;math&gt;\mathrm{true},&lt;/math&gt; then &lt;math&gt;f^{-1}(1)&lt;/math&gt; is called the ''fiber of truth'' in the proposition &lt;math&gt;f.&lt;/math&gt;  Frequent mention of this fiber makes it useful to have a shorter way of referring to it.  This leads to the definition of the notation &lt;math&gt;[|f|] = f^{-1}(1)&lt;/math&gt; for the fiber of truth in the proposition &lt;math&gt;f.&lt;/math&gt;

; Singular boolean function
: A ''singular boolean function'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a boolean function whose fiber of &lt;math&gt;1&lt;/math&gt; is a single point of &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular proposition
: In the interpretation where &lt;math&gt;1&lt;/math&gt; equals &lt;math&gt;\mathrm{true},&lt;/math&gt; a singular boolean function is called a ''singular proposition''.

: Singular boolean functions and singular propositions serve as functional or logical representatives of the points in &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular conjunction
: A ''singular conjunction'' in &lt;math&gt;\mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a conjunction of &lt;math&gt;k&lt;/math&gt; literals that includes just one conjunct of the pair &lt;math&gt;\{ x_j, ~\nu(x_j) \}&lt;/math&gt; for each &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

: A singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be expressed as a singular conjunction:

{| align=&quot;center&quot; cellspacing&quot;10&quot; width=&quot;90%&quot;
| height=&quot;36&quot; | &lt;math&gt;s ~=~ e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;,
|-
|
&lt;math&gt;\begin{array}{llll}
\text{where} &amp; e_j &amp; = &amp; x_j
\\[6pt]
\text{or}    &amp; e_j &amp; = &amp; \nu (x_j),
\\[6pt]
\text{for}   &amp; j   &amp; = &amp; 1 ~\text{to}~ k.
\end{array}&lt;/math&gt;
|}

==Resources==

* [[Logic Syllabus]]

* [http://atlas.wolfram.com/ Wolfram Atlas of Simple Programs]
** [http://atlas.wolfram.com/01/01/ Elementary Cellular Automata Rules (ECARs)]
** [http://atlas.wolfram.com/01/01/rulelist.html ECAR Index]
** [http://atlas.wolfram.com/01/01/views/3/TableView.html ECAR Icons]
** [http://atlas.wolfram.com/01/01/views/87/TableView.html ECAR Examples]
** [http://atlas.wolfram.com/01/01/views/172/TableView.html ECAR Formulas]

[[Category:Automata theory]]
[[Category:Boolean algebra]]
[[Category:Boolean functions]]
[[Category:Combinatorics]]
[[Category:Computation theory]]
[[Category:Cybernetics]]
[[Category:Differential logic]]
[[Category:Discrete mathematics]]
[[Category:Equational inference]]
[[Category:Graph theory]]
[[Category:Logic]]
[[Category:Logical graphs]]
[[Category:Neural networks]]
[[Category:Peirce, Charles Sanders]]
[[Category:Propositional calculus]]
[[Category:Semiotics]]
[[Category:Set theory]]
[[Category:Visualization]]</text>
      <sha1>rhoh4t9s1g9jwx0gho7l2mf007973tq</sha1>
    </revision>
    <revision>
      <id>2833623</id>
      <parentid>2833619</parentid>
      <timestamp>2026-09-17T14:54:06Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <comment>/* Initial definition */ adjust {| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;</comment>
      <origin>2833623</origin>
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      <format>text/x-wiki</format>
      <text bytes="18839" sha1="65f7nviviugn75j5cs01hu9zm1ego02" xml:space="preserve">{{font|size=medium|&amp;#9758;}} This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

A '''minimal negation operator''' &lt;math&gt;(\nu)&lt;/math&gt; is a logical connective which says &amp;ldquo;just one false&amp;rdquo; of its logical arguments.&amp;nbsp; The first four cases are described below.

&lt;ol start=&quot;0&quot;&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If the list of arguments is empty, as expressed in the form &lt;math&gt;\nu(),&lt;/math&gt; then it cannot be true that exactly one of the arguments is false, so &lt;math&gt;\nu() = \mathrm{false}.&lt;/math&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; is the only argument then &lt;math&gt;\nu(p)&lt;/math&gt; says that &lt;math&gt;p&lt;/math&gt; is false, so &lt;math&gt;\nu(p)&lt;/math&gt; expresses the logical negation of the proposition &lt;math&gt;p.&lt;/math&gt;&amp;nbsp; Written in several different notations, we have the following equivalent expressions.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p) ~=~ \mathrm{not}(p) ~=~ \lnot p ~=~ \tilde{p} ~=~ p^{\prime}&lt;/math&gt;&lt;/p&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; and &lt;math&gt;q&lt;/math&gt; are the only two arguments then &lt;math&gt;\nu(p, q)&lt;/math&gt; says that exactly one of &lt;math&gt;p, q&lt;/math&gt; is false, so &lt;math&gt;\nu(p, q)&lt;/math&gt; says the same thing as &lt;math&gt;p \neq q.&lt;/math&gt;  Expressing &lt;math&gt;\nu(p, q)&lt;/math&gt; in terms of ands &lt;math&gt;(\cdot),&lt;/math&gt; ors &lt;math&gt;(\lor),&lt;/math&gt; and nots &lt;math&gt;(\tilde{~})&lt;/math&gt; gives the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p} \cdot q ~\lor~ p \cdot \tilde{q}&lt;/math&gt;&lt;/p&gt;

It is permissible to omit the dot &lt;math&gt;(\cdot)&lt;/math&gt; in contexts where it is understood, giving the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p}q \lor p\tilde{q}&lt;/math&gt;&lt;/p&gt;

The venn diagram for &lt;math&gt;\nu(p, q)&lt;/math&gt; is shown in Figure&amp;nbsp;1.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 1.}~~\nu(p, q)&lt;/math&gt;&lt;/p&gt;
|}
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
The venn diagram for &lt;math&gt;\nu(p, q, r)&lt;/math&gt; is shown in Figure&amp;nbsp;2.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 2.}~~\nu(p, q, r)&lt;/math&gt;&lt;/p&gt;
|}

The center cell is the region where all three arguments &lt;math&gt;p, q, r&lt;/math&gt; hold true, so &lt;math&gt;\nu(p, q, r)&lt;/math&gt; holds true in just the three neighboring cells.&amp;nbsp; In other words:

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q, r) ~=~ \tilde{p}qr \lor p\tilde{q}r \lor pq\tilde{r}&lt;/math&gt;&lt;/p&gt;

&lt;/li&gt;&lt;/ol&gt;

==Initial definition==

The '''minimal negation operator''' &lt;math&gt;\nu&lt;/math&gt; is a [[multigrade operator]] &lt;math&gt;(\nu_k)_{k \in \mathbb{N}}&lt;/math&gt; where each &lt;math&gt;\nu_k&lt;/math&gt; is a &lt;math&gt;k&lt;/math&gt;-ary [[boolean function]] defined by the rule that &lt;math&gt;\nu_k (x_1, \ldots , x_k) = 1&lt;/math&gt; if and only if exactly one of the arguments &lt;math&gt;x_j&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;

In contexts where the initial letter &lt;math&gt;\nu&lt;/math&gt; is understood, the minimal negation operators can be indicated by argument lists in parentheses.&amp;nbsp; In the following text a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, &lt;math&gt;\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} = \nu (x, y, z).&lt;/math&gt;

The first four members of this family of operators are shown below.&amp;nbsp; The third and fourth columns give paraphrases in two other notations, where tildes and primes, respectively, indicate logical negation.

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(x)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x^\prime
\\[6pt]
\texttt{(x, y)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x^\prime y \lor x y^\prime
\\[6pt]
\texttt{(x, y, z)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x^\prime y z \lor x y^\prime z \lor x y z^\prime
\end{matrix}&lt;/math&gt;
|}

==Formal definition==

To express the general case of &lt;math&gt;\nu_k&lt;/math&gt; in terms of familiar operations, it helps to introduce an intermediary concept:

'''Definition.'''&amp;nbsp; Let the function &lt;math&gt;\lnot_j : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; be defined for each integer &lt;math&gt;j&lt;/math&gt; in the interval &lt;math&gt;[1, k]&lt;/math&gt; by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\lnot_j (x_1, \ldots, x_j, \ldots, x_k) ~=~ x_1 \land \ldots \land x_{j-1} \land \lnot x_j \land x_{j+1} \land \ldots \land x_k.&lt;/math&gt;
|}

Then &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; is defined by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\nu_k (x_1, \ldots, x_k) ~=~ \lnot_1 (x_1, \ldots, x_k) \lor \ldots \lor \lnot_j (x_1, \ldots, x_k) \lor \ldots \lor \lnot_k (x_1, \ldots, x_k).&lt;/math&gt;
|}

If we take the boolean product &lt;math&gt;x_1 \cdot \ldots \cdot x_k&lt;/math&gt; or the logical conjunction &lt;math&gt;x_1 \land \ldots \land x_k&lt;/math&gt; to indicate the point &lt;math&gt;x = (x_1, \ldots, x_k)&lt;/math&gt; in the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; then the minimal negation &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; indicates the set of points in &lt;math&gt;\mathbb{B}^k&lt;/math&gt; that differ from &lt;math&gt;x&lt;/math&gt; in exactly one coordinate.&amp;nbsp; This makes &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; a discrete functional analogue of a point-omitted neighborhood in ordinary real analysis, more exactly, a point-omitted distance-one neighborhood.&amp;nbsp; In this light, the minimal negation operator can be recognized as a differential construction, an observation that opens a very wide field.

The remainder of this discussion proceeds on the algebraic convention that the plus sign &lt;math&gt;(+)&lt;/math&gt; and the summation symbol &lt;math&gt;(\textstyle\sum)&lt;/math&gt; both refer to addition mod 2.&amp;nbsp; Unless otherwise noted, the boolean domain &lt;math&gt;\mathbb{B} = \{ 0, 1 \}&lt;/math&gt; is interpreted for logic in such a way that &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;&amp;nbsp; This has the following consequences:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;x + y&lt;/math&gt; is a function equivalent to the exclusive disjunction of &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y,&lt;/math&gt; while its fiber of 1 is the relation of inequality between &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;\textstyle\sum_{j=1}^k x_j&lt;/math&gt; maps the bit sequence &lt;math&gt;(x_1, \ldots, x_k)&lt;/math&gt; to its ''parity''.
|}

The following properties of the minimal negation operators &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; may be noted:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The function &lt;math&gt;\texttt{(x, y)}&lt;/math&gt; is the same as that associated with the operation &lt;math&gt;x + y&lt;/math&gt; and the relation &lt;math&gt;x \ne y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| In contrast, &lt;math&gt;\texttt{(x, y, z)}&lt;/math&gt; is not identical to &lt;math&gt;x + y + z.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| More generally, the function &lt;math&gt;\nu_k (x_1, \dots, x_k)&lt;/math&gt; for &lt;math&gt;k &gt; 2&lt;/math&gt; is not identical to the boolean sum &lt;math&gt;\textstyle\sum_{j=1}^k x_j.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The inclusive disjunctions indicated for the &lt;math&gt;\nu_k&lt;/math&gt; of more than one argument may be replaced with exclusive disjunctions without affecting the meaning since the terms in disjunction are already disjoint.
|}

==Truth tables==

Table&amp;nbsp;3 is a [[truth table]] for the sixteen boolean functions of type &lt;math&gt;f : \mathbb{B}^3 \to \mathbb{B}&lt;/math&gt; whose fibers of 1 are either the boundaries of points in &lt;math&gt;\mathbb{B}^3&lt;/math&gt; or the complements of those boundaries.

&lt;br&gt;

{| align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;8&quot; cellspacing=&quot;0&quot; style=&quot;text-align:center; width:70%&quot;
|+ &lt;math&gt;\text{Table 3.} ~~ \text{Logical Boundaries and Their Complements}&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &lt;math&gt;\mathcal{L}_1&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_2&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_3&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_4&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;p\colon&lt;/math&gt;
| &lt;math&gt;1~1~1~1~0~0~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;q\colon&lt;/math&gt;
| &lt;math&gt;1~1~0~0~1~1~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;r\colon&lt;/math&gt;
| &lt;math&gt;1~0~1~0~1~0~1~0&lt;/math&gt;
| &amp;nbsp;
|-
|
&lt;math&gt;\begin{matrix}
f_{104}
\\[4pt]
f_{148}
\\[4pt]
f_{146}
\\[4pt]
f_{97}
\\[4pt]
f_{134}
\\[4pt]
f_{73}
\\[4pt]
f_{41}
\\[4pt]
f_{22}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{01101000}
\\[4pt]
f_{10010100}
\\[4pt]
f_{10010010}
\\[4pt]
f_{01100001}
\\[4pt]
f_{10000110}
\\[4pt]
f_{01001001}
\\[4pt]
f_{00101001}
\\[4pt]
f_{00010110}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
0~1~1~0~1~0~0~0
\\[4pt]
1~0~0~1~0~1~0~0
\\[4pt]
1~0~0~1~0~0~1~0
\\[4pt]
0~1~1~0~0~0~0~1
\\[4pt]
1~0~0~0~0~1~1~0
\\[4pt]
0~1~0~0~1~0~0~1
\\[4pt]
0~0~1~0~1~0~0~1
\\[4pt]
0~0~0~1~0~1~1~0
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(}~p~\texttt{,}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,}~q~\texttt{,}(r\texttt{))}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),(}r\texttt{))}
\end{matrix}&lt;/math&gt;
|-
|
&lt;math&gt;\begin{matrix}
f_{233}
\\[4pt]
f_{214}
\\[4pt]
f_{182}
\\[4pt]
f_{121}
\\[4pt]
f_{158}
\\[4pt]
f_{109}
\\[4pt]
f_{107}
\\[4pt]
f_{151}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{11101001}
\\[4pt]
f_{11010110}
\\[4pt]
f_{10110110}
\\[4pt]
f_{01111001}
\\[4pt]
f_{10011110}
\\[4pt]
f_{01101101}
\\[4pt]
f_{01101011}
\\[4pt]
f_{10010111}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
1~1~1~0~1~0~0~1
\\[4pt]
1~1~0~1~0~1~1~0
\\[4pt]
1~0~1~1~0~1~1~0
\\[4pt]
0~1~1~1~1~0~0~1
\\[4pt]
1~0~0~1~1~1~1~0
\\[4pt]
0~1~1~0~1~1~0~1
\\[4pt]
0~1~1~0~1~0~1~1
\\[4pt]
1~0~0~1~0~1~1~1
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(((}p\texttt{),(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,}~r~\texttt{))}
\end{matrix}&lt;/math&gt;
|}

&lt;br&gt;

==Charts and graphs==

This Section focuses on visual representations of minimal negation operators.  A few bits of terminology are useful in describing the pictures, but the formal details are tedious reading, and may be familiar to many readers, so the full definitions of the terms marked in ''italics'' are relegated to a Glossary at the end of the article.

Two ways of visualizing the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; of &lt;math&gt;2^k&lt;/math&gt; points are the ''hypercube'' picture and the ''venn diagram'' picture.  The hypercube picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique point of the &lt;math&gt;k&lt;/math&gt;-dimensional hypercube.  The venn diagram picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique &amp;ldquo;cell&amp;rdquo; of the venn diagram on &lt;math&gt;k&lt;/math&gt; &amp;ldquo;circles&amp;rdquo;.

In addition, each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' &lt;math&gt;[|s|]&lt;/math&gt; of a ''singular proposition'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; and thus it is the unique point where a ''singular conjunction'' of &lt;math&gt;k&lt;/math&gt; ''literals'' is &lt;math&gt;1.&lt;/math&gt;

For example, consider two cases at opposite vertices of the cube:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(1, 1, \ldots , 1, 1)&lt;/math&gt; with all 1's as coordinates is the point where the conjunction of all posited variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;x_1 ~ x_2 ~\ldots~ x_{n-1} ~ x_n ~=~ 1.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(0, 0, \ldots , 0, 0)&lt;/math&gt; with all 0's as coordinates is the point where the conjunction of all negated variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;\texttt{(} x_1 \texttt{)(} x_2 \texttt{)} \ldots \texttt{(} x_{n-1} \texttt{)(} x_n \texttt{)} ~=~ 1.&lt;/math&gt;
|}

To pass from these limiting examples to the general case, observe that a singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be given canonical expression as a conjunction of literals, &lt;math&gt;s = e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;.  Then the proposition &lt;math&gt;\nu (e_1, e_2, \ldots, e_{k-1}, e_k)&lt;/math&gt; is &lt;math&gt;1&lt;/math&gt; on the points adjacent to the point where &lt;math&gt;s&lt;/math&gt; is &lt;math&gt;1,&lt;/math&gt; and 0 everywhere else on the cube.

For example, consider the case where &lt;math&gt;k = 3.&lt;/math&gt;  Then the minimal negation operation &lt;math&gt;\nu (p, q, r)&lt;/math&gt; &amp;mdash; written more simply as &lt;math&gt;\texttt{(p, q, r)}&lt;/math&gt; &amp;mdash; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 4.}~~\texttt{(p, q, r)}&lt;/math&gt;&lt;/p&gt;
|}

For a contrasting example, the boolean function expressed by the form &lt;math&gt;\texttt{((p),(q),(r))}&lt;/math&gt; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram ((P),(Q),(R)).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 5.}~~\texttt{((p),(q),(r))}&lt;/math&gt;&lt;/p&gt;
|}

==Glossary of basic terms==

; Boolean domain
: A ''[[boolean domain]]'' &lt;math&gt;\mathbb{B}&lt;/math&gt; is a generic 2-element set, for example, &lt;math&gt;\mathbb{B} = \{ 0, 1 \},&lt;/math&gt; whose elements are interpreted as logical values, usually but not invariably with &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;

; Boolean variable
: A ''boolean variable'' &lt;math&gt;x&lt;/math&gt; is a variable that takes its value from a boolean domain, as &lt;math&gt;x \in \mathbb{B}.&lt;/math&gt;

; Proposition
: In situations where boolean values are interpreted as logical values, a [[boolean-valued function]] &lt;math&gt;f : X \to \mathbb{B}&lt;/math&gt; or a [[boolean function]] &lt;math&gt;g : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is frequently called a ''proposition''.

; Basis element, Coordinate projection
: Given a sequence of &lt;math&gt;k&lt;/math&gt; boolean variables, &lt;math&gt;x_1, \ldots, x_k,&lt;/math&gt; each variable &lt;math&gt;x_j&lt;/math&gt; may be treated either as a ''basis element'' of the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; or as a ''coordinate projection'' &lt;math&gt;x_j : \mathbb{B}^k \to \mathbb{B}.&lt;/math&gt;

; Basic proposition
: This means that the set of objects &lt;math&gt;\{ x_j : 1 \le j \le k \}&lt;/math&gt; is a set of boolean functions &lt;math&gt;\{ x_j : \mathbb{B}^k \to \mathbb{B} \}&lt;/math&gt; subject to logical interpretation as a set of ''basic propositions'' that collectively generate the complete set of &lt;math&gt;2^{2^k}&lt;/math&gt; propositions over &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Literal
: A ''literal'' is one of the &lt;math&gt;2k&lt;/math&gt; propositions &lt;math&gt;x_1, \ldots, x_k, \texttt{(} x_1 \texttt{)}, \ldots, \texttt{(} x_k \texttt{)},&lt;/math&gt; in other words, either a ''posited'' basic proposition &lt;math&gt;x_j&lt;/math&gt; or a ''negated'' basic proposition &lt;math&gt;\texttt{(} x_j \texttt{)},&lt;/math&gt; for some &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

; Fiber
: In mathematics generally, the ''[[fiber (mathematics)|fiber]]'' of a point &lt;math&gt;y \in Y&lt;/math&gt; under a function &lt;math&gt;f : X \to Y&lt;/math&gt; is defined as the inverse image &lt;math&gt;f^{-1}(y) \subseteq X.&lt;/math&gt;

: In the case of a boolean function &lt;math&gt;f : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; there are just two fibers:
: The fiber of &lt;math&gt;0&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(0),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;
: The fiber of &lt;math&gt;1&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(1),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;1.&lt;/math&gt;

; Fiber of truth
: When &lt;math&gt;1&lt;/math&gt; is interpreted as the logical value &lt;math&gt;\mathrm{true},&lt;/math&gt; then &lt;math&gt;f^{-1}(1)&lt;/math&gt; is called the ''fiber of truth'' in the proposition &lt;math&gt;f.&lt;/math&gt;  Frequent mention of this fiber makes it useful to have a shorter way of referring to it.  This leads to the definition of the notation &lt;math&gt;[|f|] = f^{-1}(1)&lt;/math&gt; for the fiber of truth in the proposition &lt;math&gt;f.&lt;/math&gt;

; Singular boolean function
: A ''singular boolean function'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a boolean function whose fiber of &lt;math&gt;1&lt;/math&gt; is a single point of &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular proposition
: In the interpretation where &lt;math&gt;1&lt;/math&gt; equals &lt;math&gt;\mathrm{true},&lt;/math&gt; a singular boolean function is called a ''singular proposition''.

: Singular boolean functions and singular propositions serve as functional or logical representatives of the points in &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular conjunction
: A ''singular conjunction'' in &lt;math&gt;\mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a conjunction of &lt;math&gt;k&lt;/math&gt; literals that includes just one conjunct of the pair &lt;math&gt;\{ x_j, ~\nu(x_j) \}&lt;/math&gt; for each &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

: A singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be expressed as a singular conjunction:

{| align=&quot;center&quot; cellspacing&quot;10&quot; width=&quot;90%&quot;
| height=&quot;36&quot; | &lt;math&gt;s ~=~ e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;,
|-
|
&lt;math&gt;\begin{array}{llll}
\text{where} &amp; e_j &amp; = &amp; x_j
\\[6pt]
\text{or}    &amp; e_j &amp; = &amp; \nu (x_j),
\\[6pt]
\text{for}   &amp; j   &amp; = &amp; 1 ~\text{to}~ k.
\end{array}&lt;/math&gt;
|}

==Resources==

* [[Logic Syllabus]]

* [http://atlas.wolfram.com/ Wolfram Atlas of Simple Programs]
** [http://atlas.wolfram.com/01/01/ Elementary Cellular Automata Rules (ECARs)]
** [http://atlas.wolfram.com/01/01/rulelist.html ECAR Index]
** [http://atlas.wolfram.com/01/01/views/3/TableView.html ECAR Icons]
** [http://atlas.wolfram.com/01/01/views/87/TableView.html ECAR Examples]
** [http://atlas.wolfram.com/01/01/views/172/TableView.html ECAR Formulas]

[[Category:Automata theory]]
[[Category:Boolean algebra]]
[[Category:Boolean functions]]
[[Category:Combinatorics]]
[[Category:Computation theory]]
[[Category:Cybernetics]]
[[Category:Differential logic]]
[[Category:Discrete mathematics]]
[[Category:Equational inference]]
[[Category:Graph theory]]
[[Category:Logic]]
[[Category:Logical graphs]]
[[Category:Neural networks]]
[[Category:Peirce, Charles Sanders]]
[[Category:Propositional calculus]]
[[Category:Semiotics]]
[[Category:Set theory]]
[[Category:Visualization]]</text>
      <sha1>65f7nviviugn75j5cs01hu9zm1ego02</sha1>
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      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
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      <comment>use format &lt;math&gt;\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} = \nu (x, y, z)&lt;/math&gt; etc.</comment>
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      <text bytes="18902" sha1="3plv1d16vb4ft9grgovhylktbriusxm" xml:space="preserve">{{font|size=medium|&amp;#9758;}} This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

A '''minimal negation operator''' &lt;math&gt;(\nu)&lt;/math&gt; is a logical connective which says &amp;ldquo;just one false&amp;rdquo; of its logical arguments.&amp;nbsp; The first four cases are described below.

&lt;ol start=&quot;0&quot;&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If the list of arguments is empty, as expressed in the form &lt;math&gt;\nu(),&lt;/math&gt; then it cannot be true that exactly one of the arguments is false, so &lt;math&gt;\nu() = \mathrm{false}.&lt;/math&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; is the only argument then &lt;math&gt;\nu(p)&lt;/math&gt; says that &lt;math&gt;p&lt;/math&gt; is false, so &lt;math&gt;\nu(p)&lt;/math&gt; expresses the logical negation of the proposition &lt;math&gt;p.&lt;/math&gt;&amp;nbsp; Written in several different notations, we have the following equivalent expressions.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p) ~=~ \mathrm{not}(p) ~=~ \lnot p ~=~ \tilde{p} ~=~ p^{\prime}&lt;/math&gt;&lt;/p&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; and &lt;math&gt;q&lt;/math&gt; are the only two arguments then &lt;math&gt;\nu(p, q)&lt;/math&gt; says that exactly one of &lt;math&gt;p, q&lt;/math&gt; is false, so &lt;math&gt;\nu(p, q)&lt;/math&gt; says the same thing as &lt;math&gt;p \neq q.&lt;/math&gt;  Expressing &lt;math&gt;\nu(p, q)&lt;/math&gt; in terms of ands &lt;math&gt;(\cdot),&lt;/math&gt; ors &lt;math&gt;(\lor),&lt;/math&gt; and nots &lt;math&gt;(\tilde{~})&lt;/math&gt; gives the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p} \cdot q ~\lor~ p \cdot \tilde{q}&lt;/math&gt;&lt;/p&gt;

It is permissible to omit the dot &lt;math&gt;(\cdot)&lt;/math&gt; in contexts where it is understood, giving the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p}q \lor p\tilde{q}&lt;/math&gt;&lt;/p&gt;

The venn diagram for &lt;math&gt;\nu(p, q)&lt;/math&gt; is shown in Figure&amp;nbsp;1.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 1.}~~\nu(p, q)&lt;/math&gt;&lt;/p&gt;
|}
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
The venn diagram for &lt;math&gt;\nu(p, q, r)&lt;/math&gt; is shown in Figure&amp;nbsp;2.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 2.}~~\nu(p, q, r)&lt;/math&gt;&lt;/p&gt;
|}

The center cell is the region where all three arguments &lt;math&gt;p, q, r&lt;/math&gt; hold true, so &lt;math&gt;\nu(p, q, r)&lt;/math&gt; holds true in just the three neighboring cells.&amp;nbsp; In other words:

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q, r) ~=~ \tilde{p}qr \lor p\tilde{q}r \lor pq\tilde{r}&lt;/math&gt;&lt;/p&gt;

&lt;/li&gt;&lt;/ol&gt;

==Initial definition==

The '''minimal negation operator''' &lt;math&gt;\nu&lt;/math&gt; is a [[multigrade operator]] &lt;math&gt;(\nu_k)_{k \in \mathbb{N}}&lt;/math&gt; where each &lt;math&gt;\nu_k&lt;/math&gt; is a &lt;math&gt;k&lt;/math&gt;-ary [[boolean function]] defined by the rule that &lt;math&gt;\nu_k (x_1, \ldots , x_k) = 1&lt;/math&gt; if and only if exactly one of the arguments &lt;math&gt;x_j&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;

In contexts where the initial letter &lt;math&gt;\nu&lt;/math&gt; is understood, the minimal negation operators can be indicated by argument lists in parentheses.&amp;nbsp; In the following text a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, &lt;math&gt;\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} = \nu (x, y, z).&lt;/math&gt;

The first four members of this family of operators are shown below.&amp;nbsp; The third and fourth columns give paraphrases in two other notations, where tildes and primes, respectively, indicate logical negation.

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(} x \texttt{)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x^\prime
\\[6pt]
\texttt{(} x \texttt{,} y \texttt{)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x^\prime y \lor x y^\prime
\\[6pt]
\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x^\prime y z \lor x y^\prime z \lor x y z^\prime
\end{matrix}&lt;/math&gt;
|}

==Formal definition==

To express the general case of &lt;math&gt;\nu_k&lt;/math&gt; in terms of familiar operations, it helps to introduce an intermediary concept:

'''Definition.'''&amp;nbsp; Let the function &lt;math&gt;\lnot_j : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; be defined for each integer &lt;math&gt;j&lt;/math&gt; in the interval &lt;math&gt;[1, k]&lt;/math&gt; by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\lnot_j (x_1, \ldots, x_j, \ldots, x_k) ~=~ x_1 \land \ldots \land x_{j-1} \land \lnot x_j \land x_{j+1} \land \ldots \land x_k.&lt;/math&gt;
|}

Then &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; is defined by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\nu_k (x_1, \ldots, x_k) ~=~ \lnot_1 (x_1, \ldots, x_k) \lor \ldots \lor \lnot_j (x_1, \ldots, x_k) \lor \ldots \lor \lnot_k (x_1, \ldots, x_k).&lt;/math&gt;
|}

If we take the boolean product &lt;math&gt;x_1 \cdot \ldots \cdot x_k&lt;/math&gt; or the logical conjunction &lt;math&gt;x_1 \land \ldots \land x_k&lt;/math&gt; to indicate the point &lt;math&gt;x = (x_1, \ldots, x_k)&lt;/math&gt; in the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; then the minimal negation &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; indicates the set of points in &lt;math&gt;\mathbb{B}^k&lt;/math&gt; that differ from &lt;math&gt;x&lt;/math&gt; in exactly one coordinate.&amp;nbsp; This makes &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; a discrete functional analogue of a point-omitted neighborhood in ordinary real analysis, more exactly, a point-omitted distance-one neighborhood.&amp;nbsp; In this light, the minimal negation operator can be recognized as a differential construction, an observation that opens a very wide field.

The remainder of this discussion proceeds on the algebraic convention that the plus sign &lt;math&gt;(+)&lt;/math&gt; and the summation symbol &lt;math&gt;(\textstyle\sum)&lt;/math&gt; both refer to addition mod 2.&amp;nbsp; Unless otherwise noted, the boolean domain &lt;math&gt;\mathbb{B} = \{ 0, 1 \}&lt;/math&gt; is interpreted for logic in such a way that &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;&amp;nbsp; This has the following consequences:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;x + y&lt;/math&gt; is a function equivalent to the exclusive disjunction of &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y,&lt;/math&gt; while its fiber of 1 is the relation of inequality between &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;\textstyle\sum_{j=1}^k x_j&lt;/math&gt; maps the bit sequence &lt;math&gt;(x_1, \ldots, x_k)&lt;/math&gt; to its ''parity''.
|}

The following properties of the minimal negation operators &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; may be noted:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The function &lt;math&gt;\texttt{(x, y)}&lt;/math&gt; is the same as that associated with the operation &lt;math&gt;x + y&lt;/math&gt; and the relation &lt;math&gt;x \ne y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| In contrast, &lt;math&gt;\texttt{(x, y, z)}&lt;/math&gt; is not identical to &lt;math&gt;x + y + z.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| More generally, the function &lt;math&gt;\nu_k (x_1, \dots, x_k)&lt;/math&gt; for &lt;math&gt;k &gt; 2&lt;/math&gt; is not identical to the boolean sum &lt;math&gt;\textstyle\sum_{j=1}^k x_j.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The inclusive disjunctions indicated for the &lt;math&gt;\nu_k&lt;/math&gt; of more than one argument may be replaced with exclusive disjunctions without affecting the meaning since the terms in disjunction are already disjoint.
|}

==Truth tables==

Table&amp;nbsp;3 is a [[truth table]] for the sixteen boolean functions of type &lt;math&gt;f : \mathbb{B}^3 \to \mathbb{B}&lt;/math&gt; whose fibers of 1 are either the boundaries of points in &lt;math&gt;\mathbb{B}^3&lt;/math&gt; or the complements of those boundaries.

&lt;br&gt;

{| align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;8&quot; cellspacing=&quot;0&quot; style=&quot;text-align:center; width:70%&quot;
|+ &lt;math&gt;\text{Table 3.} ~~ \text{Logical Boundaries and Their Complements}&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &lt;math&gt;\mathcal{L}_1&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_2&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_3&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_4&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;p\colon&lt;/math&gt;
| &lt;math&gt;1~1~1~1~0~0~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;q\colon&lt;/math&gt;
| &lt;math&gt;1~1~0~0~1~1~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;r\colon&lt;/math&gt;
| &lt;math&gt;1~0~1~0~1~0~1~0&lt;/math&gt;
| &amp;nbsp;
|-
|
&lt;math&gt;\begin{matrix}
f_{104}
\\[4pt]
f_{148}
\\[4pt]
f_{146}
\\[4pt]
f_{97}
\\[4pt]
f_{134}
\\[4pt]
f_{73}
\\[4pt]
f_{41}
\\[4pt]
f_{22}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{01101000}
\\[4pt]
f_{10010100}
\\[4pt]
f_{10010010}
\\[4pt]
f_{01100001}
\\[4pt]
f_{10000110}
\\[4pt]
f_{01001001}
\\[4pt]
f_{00101001}
\\[4pt]
f_{00010110}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
0~1~1~0~1~0~0~0
\\[4pt]
1~0~0~1~0~1~0~0
\\[4pt]
1~0~0~1~0~0~1~0
\\[4pt]
0~1~1~0~0~0~0~1
\\[4pt]
1~0~0~0~0~1~1~0
\\[4pt]
0~1~0~0~1~0~0~1
\\[4pt]
0~0~1~0~1~0~0~1
\\[4pt]
0~0~0~1~0~1~1~0
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(}~p~\texttt{,}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,}~q~\texttt{,}(r\texttt{))}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),(}r\texttt{))}
\end{matrix}&lt;/math&gt;
|-
|
&lt;math&gt;\begin{matrix}
f_{233}
\\[4pt]
f_{214}
\\[4pt]
f_{182}
\\[4pt]
f_{121}
\\[4pt]
f_{158}
\\[4pt]
f_{109}
\\[4pt]
f_{107}
\\[4pt]
f_{151}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{11101001}
\\[4pt]
f_{11010110}
\\[4pt]
f_{10110110}
\\[4pt]
f_{01111001}
\\[4pt]
f_{10011110}
\\[4pt]
f_{01101101}
\\[4pt]
f_{01101011}
\\[4pt]
f_{10010111}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
1~1~1~0~1~0~0~1
\\[4pt]
1~1~0~1~0~1~1~0
\\[4pt]
1~0~1~1~0~1~1~0
\\[4pt]
0~1~1~1~1~0~0~1
\\[4pt]
1~0~0~1~1~1~1~0
\\[4pt]
0~1~1~0~1~1~0~1
\\[4pt]
0~1~1~0~1~0~1~1
\\[4pt]
1~0~0~1~0~1~1~1
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(((}p\texttt{),(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,}~r~\texttt{))}
\end{matrix}&lt;/math&gt;
|}

&lt;br&gt;

==Charts and graphs==

This Section focuses on visual representations of minimal negation operators.  A few bits of terminology are useful in describing the pictures, but the formal details are tedious reading, and may be familiar to many readers, so the full definitions of the terms marked in ''italics'' are relegated to a Glossary at the end of the article.

Two ways of visualizing the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; of &lt;math&gt;2^k&lt;/math&gt; points are the ''hypercube'' picture and the ''venn diagram'' picture.  The hypercube picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique point of the &lt;math&gt;k&lt;/math&gt;-dimensional hypercube.  The venn diagram picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique &amp;ldquo;cell&amp;rdquo; of the venn diagram on &lt;math&gt;k&lt;/math&gt; &amp;ldquo;circles&amp;rdquo;.

In addition, each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' &lt;math&gt;[|s|]&lt;/math&gt; of a ''singular proposition'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; and thus it is the unique point where a ''singular conjunction'' of &lt;math&gt;k&lt;/math&gt; ''literals'' is &lt;math&gt;1.&lt;/math&gt;

For example, consider two cases at opposite vertices of the cube:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(1, 1, \ldots , 1, 1)&lt;/math&gt; with all 1's as coordinates is the point where the conjunction of all posited variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;x_1 ~ x_2 ~\ldots~ x_{n-1} ~ x_n ~=~ 1.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(0, 0, \ldots , 0, 0)&lt;/math&gt; with all 0's as coordinates is the point where the conjunction of all negated variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;\texttt{(} x_1 \texttt{)(} x_2 \texttt{)} \ldots \texttt{(} x_{n-1} \texttt{)(} x_n \texttt{)} ~=~ 1.&lt;/math&gt;
|}

To pass from these limiting examples to the general case, observe that a singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be given canonical expression as a conjunction of literals, &lt;math&gt;s = e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;.  Then the proposition &lt;math&gt;\nu (e_1, e_2, \ldots, e_{k-1}, e_k)&lt;/math&gt; is &lt;math&gt;1&lt;/math&gt; on the points adjacent to the point where &lt;math&gt;s&lt;/math&gt; is &lt;math&gt;1,&lt;/math&gt; and 0 everywhere else on the cube.

For example, consider the case where &lt;math&gt;k = 3.&lt;/math&gt;  Then the minimal negation operation &lt;math&gt;\nu (p, q, r)&lt;/math&gt; &amp;mdash; written more simply as &lt;math&gt;\texttt{(p, q, r)}&lt;/math&gt; &amp;mdash; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 4.}~~\texttt{(p, q, r)}&lt;/math&gt;&lt;/p&gt;
|}

For a contrasting example, the boolean function expressed by the form &lt;math&gt;\texttt{((p),(q),(r))}&lt;/math&gt; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram ((P),(Q),(R)).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 5.}~~\texttt{((p),(q),(r))}&lt;/math&gt;&lt;/p&gt;
|}

==Glossary of basic terms==

; Boolean domain
: A ''[[boolean domain]]'' &lt;math&gt;\mathbb{B}&lt;/math&gt; is a generic 2-element set, for example, &lt;math&gt;\mathbb{B} = \{ 0, 1 \},&lt;/math&gt; whose elements are interpreted as logical values, usually but not invariably with &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;

; Boolean variable
: A ''boolean variable'' &lt;math&gt;x&lt;/math&gt; is a variable that takes its value from a boolean domain, as &lt;math&gt;x \in \mathbb{B}.&lt;/math&gt;

; Proposition
: In situations where boolean values are interpreted as logical values, a [[boolean-valued function]] &lt;math&gt;f : X \to \mathbb{B}&lt;/math&gt; or a [[boolean function]] &lt;math&gt;g : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is frequently called a ''proposition''.

; Basis element, Coordinate projection
: Given a sequence of &lt;math&gt;k&lt;/math&gt; boolean variables, &lt;math&gt;x_1, \ldots, x_k,&lt;/math&gt; each variable &lt;math&gt;x_j&lt;/math&gt; may be treated either as a ''basis element'' of the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; or as a ''coordinate projection'' &lt;math&gt;x_j : \mathbb{B}^k \to \mathbb{B}.&lt;/math&gt;

; Basic proposition
: This means that the set of objects &lt;math&gt;\{ x_j : 1 \le j \le k \}&lt;/math&gt; is a set of boolean functions &lt;math&gt;\{ x_j : \mathbb{B}^k \to \mathbb{B} \}&lt;/math&gt; subject to logical interpretation as a set of ''basic propositions'' that collectively generate the complete set of &lt;math&gt;2^{2^k}&lt;/math&gt; propositions over &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Literal
: A ''literal'' is one of the &lt;math&gt;2k&lt;/math&gt; propositions &lt;math&gt;x_1, \ldots, x_k, \texttt{(} x_1 \texttt{)}, \ldots, \texttt{(} x_k \texttt{)},&lt;/math&gt; in other words, either a ''posited'' basic proposition &lt;math&gt;x_j&lt;/math&gt; or a ''negated'' basic proposition &lt;math&gt;\texttt{(} x_j \texttt{)},&lt;/math&gt; for some &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

; Fiber
: In mathematics generally, the ''[[fiber (mathematics)|fiber]]'' of a point &lt;math&gt;y \in Y&lt;/math&gt; under a function &lt;math&gt;f : X \to Y&lt;/math&gt; is defined as the inverse image &lt;math&gt;f^{-1}(y) \subseteq X.&lt;/math&gt;

: In the case of a boolean function &lt;math&gt;f : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; there are just two fibers:
: The fiber of &lt;math&gt;0&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(0),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;
: The fiber of &lt;math&gt;1&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(1),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;1.&lt;/math&gt;

; Fiber of truth
: When &lt;math&gt;1&lt;/math&gt; is interpreted as the logical value &lt;math&gt;\mathrm{true},&lt;/math&gt; then &lt;math&gt;f^{-1}(1)&lt;/math&gt; is called the ''fiber of truth'' in the proposition &lt;math&gt;f.&lt;/math&gt;  Frequent mention of this fiber makes it useful to have a shorter way of referring to it.  This leads to the definition of the notation &lt;math&gt;[|f|] = f^{-1}(1)&lt;/math&gt; for the fiber of truth in the proposition &lt;math&gt;f.&lt;/math&gt;

; Singular boolean function
: A ''singular boolean function'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a boolean function whose fiber of &lt;math&gt;1&lt;/math&gt; is a single point of &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular proposition
: In the interpretation where &lt;math&gt;1&lt;/math&gt; equals &lt;math&gt;\mathrm{true},&lt;/math&gt; a singular boolean function is called a ''singular proposition''.

: Singular boolean functions and singular propositions serve as functional or logical representatives of the points in &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular conjunction
: A ''singular conjunction'' in &lt;math&gt;\mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a conjunction of &lt;math&gt;k&lt;/math&gt; literals that includes just one conjunct of the pair &lt;math&gt;\{ x_j, ~\nu(x_j) \}&lt;/math&gt; for each &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

: A singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be expressed as a singular conjunction:

{| align=&quot;center&quot; cellspacing&quot;10&quot; width=&quot;90%&quot;
| height=&quot;36&quot; | &lt;math&gt;s ~=~ e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;,
|-
|
&lt;math&gt;\begin{array}{llll}
\text{where} &amp; e_j &amp; = &amp; x_j
\\[6pt]
\text{or}    &amp; e_j &amp; = &amp; \nu (x_j),
\\[6pt]
\text{for}   &amp; j   &amp; = &amp; 1 ~\text{to}~ k.
\end{array}&lt;/math&gt;
|}

==Resources==

* [[Logic Syllabus]]

* [http://atlas.wolfram.com/ Wolfram Atlas of Simple Programs]
** [http://atlas.wolfram.com/01/01/ Elementary Cellular Automata Rules (ECARs)]
** [http://atlas.wolfram.com/01/01/rulelist.html ECAR Index]
** [http://atlas.wolfram.com/01/01/views/3/TableView.html ECAR Icons]
** [http://atlas.wolfram.com/01/01/views/87/TableView.html ECAR Examples]
** [http://atlas.wolfram.com/01/01/views/172/TableView.html ECAR Formulas]

[[Category:Automata theory]]
[[Category:Boolean algebra]]
[[Category:Boolean functions]]
[[Category:Combinatorics]]
[[Category:Computation theory]]
[[Category:Cybernetics]]
[[Category:Differential logic]]
[[Category:Discrete mathematics]]
[[Category:Equational inference]]
[[Category:Graph theory]]
[[Category:Logic]]
[[Category:Logical graphs]]
[[Category:Neural networks]]
[[Category:Peirce, Charles Sanders]]
[[Category:Propositional calculus]]
[[Category:Semiotics]]
[[Category:Set theory]]
[[Category:Visualization]]</text>
      <sha1>3plv1d16vb4ft9grgovhylktbriusxm</sha1>
    </revision>
    <revision>
      <id>2833637</id>
      <parentid>2833625</parentid>
      <timestamp>2026-09-17T17:26:40Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <comment>/* Initial definition */ use \prime + \texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} etc.</comment>
      <origin>2833637</origin>
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      <format>text/x-wiki</format>
      <text bytes="18896" sha1="6fjhbukqx2ezwc90qxudg2fn9iq9wl9" xml:space="preserve">{{font|size=medium|&amp;#9758;}} This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

A '''minimal negation operator''' &lt;math&gt;(\nu)&lt;/math&gt; is a logical connective which says &amp;ldquo;just one false&amp;rdquo; of its logical arguments.&amp;nbsp; The first four cases are described below.

&lt;ol start=&quot;0&quot;&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If the list of arguments is empty, as expressed in the form &lt;math&gt;\nu(),&lt;/math&gt; then it cannot be true that exactly one of the arguments is false, so &lt;math&gt;\nu() = \mathrm{false}.&lt;/math&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; is the only argument then &lt;math&gt;\nu(p)&lt;/math&gt; says that &lt;math&gt;p&lt;/math&gt; is false, so &lt;math&gt;\nu(p)&lt;/math&gt; expresses the logical negation of the proposition &lt;math&gt;p.&lt;/math&gt;&amp;nbsp; Written in several different notations, we have the following equivalent expressions.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p) ~=~ \mathrm{not}(p) ~=~ \lnot p ~=~ \tilde{p} ~=~ p^{\prime}&lt;/math&gt;&lt;/p&gt;
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
If &lt;math&gt;p&lt;/math&gt; and &lt;math&gt;q&lt;/math&gt; are the only two arguments then &lt;math&gt;\nu(p, q)&lt;/math&gt; says that exactly one of &lt;math&gt;p, q&lt;/math&gt; is false, so &lt;math&gt;\nu(p, q)&lt;/math&gt; says the same thing as &lt;math&gt;p \neq q.&lt;/math&gt;  Expressing &lt;math&gt;\nu(p, q)&lt;/math&gt; in terms of ands &lt;math&gt;(\cdot),&lt;/math&gt; ors &lt;math&gt;(\lor),&lt;/math&gt; and nots &lt;math&gt;(\tilde{~})&lt;/math&gt; gives the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p} \cdot q ~\lor~ p \cdot \tilde{q}&lt;/math&gt;&lt;/p&gt;

It is permissible to omit the dot &lt;math&gt;(\cdot)&lt;/math&gt; in contexts where it is understood, giving the following form.

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q) ~=~ \tilde{p}q \lor p\tilde{q}&lt;/math&gt;&lt;/p&gt;

The venn diagram for &lt;math&gt;\nu(p, q)&lt;/math&gt; is shown in Figure&amp;nbsp;1.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 1.}~~\nu(p, q)&lt;/math&gt;&lt;/p&gt;
|}
&lt;/li&gt;

&lt;li style=&quot;padding:8px&quot;&gt;
The venn diagram for &lt;math&gt;\nu(p, q, r)&lt;/math&gt; is shown in Figure&amp;nbsp;2.

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 2.}~~\nu(p, q, r)&lt;/math&gt;&lt;/p&gt;
|}

The center cell is the region where all three arguments &lt;math&gt;p, q, r&lt;/math&gt; hold true, so &lt;math&gt;\nu(p, q, r)&lt;/math&gt; holds true in just the three neighboring cells.&amp;nbsp; In other words:

&lt;p style=&quot;padding:8px; text-align:center&quot;&gt;&lt;math&gt;\nu(p, q, r) ~=~ \tilde{p}qr \lor p\tilde{q}r \lor pq\tilde{r}&lt;/math&gt;&lt;/p&gt;

&lt;/li&gt;&lt;/ol&gt;

==Initial definition==

The '''minimal negation operator''' &lt;math&gt;\nu&lt;/math&gt; is a [[multigrade operator]] &lt;math&gt;(\nu_k)_{k \in \mathbb{N}}&lt;/math&gt; where each &lt;math&gt;\nu_k&lt;/math&gt; is a &lt;math&gt;k&lt;/math&gt;-ary [[boolean function]] defined by the rule that &lt;math&gt;\nu_k (x_1, \ldots , x_k) = 1&lt;/math&gt; if and only if exactly one of the arguments &lt;math&gt;x_j&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;

In contexts where the initial letter &lt;math&gt;\nu&lt;/math&gt; is understood, the minimal negation operators can be indicated by argument lists in parentheses.&amp;nbsp; In the following text a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, &lt;math&gt;\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} = \nu (x, y, z).&lt;/math&gt;

The first four members of this family of operators are shown below.&amp;nbsp; The third and fourth columns give paraphrases in two other notations, where tildes and primes, respectively, indicate logical negation.

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(} x \texttt{)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x\prime
\\[6pt]
\texttt{(} x \texttt{,} y \texttt{)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x\prime y \lor x y\prime
\\[6pt]
\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x\prime y z \lor x y\prime z \lor x y z\prime
\end{matrix}&lt;/math&gt;
|}

==Formal definition==

To express the general case of &lt;math&gt;\nu_k&lt;/math&gt; in terms of familiar operations, it helps to introduce an intermediary concept:

'''Definition.'''&amp;nbsp; Let the function &lt;math&gt;\lnot_j : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; be defined for each integer &lt;math&gt;j&lt;/math&gt; in the interval &lt;math&gt;[1, k]&lt;/math&gt; by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\lnot_j (x_1, \ldots, x_j, \ldots, x_k) ~=~ x_1 \land \ldots \land x_{j-1} \land \lnot x_j \land x_{j+1} \land \ldots \land x_k.&lt;/math&gt;
|}

Then &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; is defined by the following equation:

{| align=&quot;center&quot; cellpadding=&quot;8&quot;
| &lt;math&gt;\nu_k (x_1, \ldots, x_k) ~=~ \lnot_1 (x_1, \ldots, x_k) \lor \ldots \lor \lnot_j (x_1, \ldots, x_k) \lor \ldots \lor \lnot_k (x_1, \ldots, x_k).&lt;/math&gt;
|}

If we take the boolean product &lt;math&gt;x_1 \cdot \ldots \cdot x_k&lt;/math&gt; or the logical conjunction &lt;math&gt;x_1 \land \ldots \land x_k&lt;/math&gt; to indicate the point &lt;math&gt;x = (x_1, \ldots, x_k)&lt;/math&gt; in the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; then the minimal negation &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; indicates the set of points in &lt;math&gt;\mathbb{B}^k&lt;/math&gt; that differ from &lt;math&gt;x&lt;/math&gt; in exactly one coordinate.&amp;nbsp; This makes &lt;math&gt;\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_k \texttt{)}&lt;/math&gt; a discrete functional analogue of a point-omitted neighborhood in ordinary real analysis, more exactly, a point-omitted distance-one neighborhood.&amp;nbsp; In this light, the minimal negation operator can be recognized as a differential construction, an observation that opens a very wide field.

The remainder of this discussion proceeds on the algebraic convention that the plus sign &lt;math&gt;(+)&lt;/math&gt; and the summation symbol &lt;math&gt;(\textstyle\sum)&lt;/math&gt; both refer to addition mod 2.&amp;nbsp; Unless otherwise noted, the boolean domain &lt;math&gt;\mathbb{B} = \{ 0, 1 \}&lt;/math&gt; is interpreted for logic in such a way that &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;&amp;nbsp; This has the following consequences:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;x + y&lt;/math&gt; is a function equivalent to the exclusive disjunction of &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y,&lt;/math&gt; while its fiber of 1 is the relation of inequality between &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The operation &lt;math&gt;\textstyle\sum_{j=1}^k x_j&lt;/math&gt; maps the bit sequence &lt;math&gt;(x_1, \ldots, x_k)&lt;/math&gt; to its ''parity''.
|}

The following properties of the minimal negation operators &lt;math&gt;{\nu_k : \mathbb{B}^k \to \mathbb{B}}&lt;/math&gt; may be noted:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The function &lt;math&gt;\texttt{(x, y)}&lt;/math&gt; is the same as that associated with the operation &lt;math&gt;x + y&lt;/math&gt; and the relation &lt;math&gt;x \ne y.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| In contrast, &lt;math&gt;\texttt{(x, y, z)}&lt;/math&gt; is not identical to &lt;math&gt;x + y + z.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| More generally, the function &lt;math&gt;\nu_k (x_1, \dots, x_k)&lt;/math&gt; for &lt;math&gt;k &gt; 2&lt;/math&gt; is not identical to the boolean sum &lt;math&gt;\textstyle\sum_{j=1}^k x_j.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The inclusive disjunctions indicated for the &lt;math&gt;\nu_k&lt;/math&gt; of more than one argument may be replaced with exclusive disjunctions without affecting the meaning since the terms in disjunction are already disjoint.
|}

==Truth tables==

Table&amp;nbsp;3 is a [[truth table]] for the sixteen boolean functions of type &lt;math&gt;f : \mathbb{B}^3 \to \mathbb{B}&lt;/math&gt; whose fibers of 1 are either the boundaries of points in &lt;math&gt;\mathbb{B}^3&lt;/math&gt; or the complements of those boundaries.

&lt;br&gt;

{| align=&quot;center&quot; border=&quot;1&quot; cellpadding=&quot;8&quot; cellspacing=&quot;0&quot; style=&quot;text-align:center; width:70%&quot;
|+ &lt;math&gt;\text{Table 3.} ~~ \text{Logical Boundaries and Their Complements}&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &lt;math&gt;\mathcal{L}_1&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_2&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_3&lt;/math&gt;
| &lt;math&gt;\mathcal{L}_4&lt;/math&gt;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;p\colon&lt;/math&gt;
| &lt;math&gt;1~1~1~1~0~0~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;q\colon&lt;/math&gt;
| &lt;math&gt;1~1~0~0~1~1~0~0&lt;/math&gt;
| &amp;nbsp;
|- style=&quot;background:ghostwhite&quot;
| &amp;nbsp;
| align=&quot;right&quot; | &lt;math&gt;r\colon&lt;/math&gt;
| &lt;math&gt;1~0~1~0~1~0~1~0&lt;/math&gt;
| &amp;nbsp;
|-
|
&lt;math&gt;\begin{matrix}
f_{104}
\\[4pt]
f_{148}
\\[4pt]
f_{146}
\\[4pt]
f_{97}
\\[4pt]
f_{134}
\\[4pt]
f_{73}
\\[4pt]
f_{41}
\\[4pt]
f_{22}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{01101000}
\\[4pt]
f_{10010100}
\\[4pt]
f_{10010010}
\\[4pt]
f_{01100001}
\\[4pt]
f_{10000110}
\\[4pt]
f_{01001001}
\\[4pt]
f_{00101001}
\\[4pt]
f_{00010110}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
0~1~1~0~1~0~0~0
\\[4pt]
1~0~0~1~0~1~0~0
\\[4pt]
1~0~0~1~0~0~1~0
\\[4pt]
0~1~1~0~0~0~0~1
\\[4pt]
1~0~0~0~0~1~1~0
\\[4pt]
0~1~0~0~1~0~0~1
\\[4pt]
0~0~1~0~1~0~0~1
\\[4pt]
0~0~0~1~0~1~1~0
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(}~p~\texttt{,}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,}~q~\texttt{,}(r\texttt{))}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{(}~p~\texttt{,(}q\texttt{),(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),}~q~\texttt{,(}r\texttt{))}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),}~r~\texttt{)}
\\[4pt]
\texttt{((}p\texttt{),(}q\texttt{),(}r\texttt{))}
\end{matrix}&lt;/math&gt;
|-
|
&lt;math&gt;\begin{matrix}
f_{233}
\\[4pt]
f_{214}
\\[4pt]
f_{182}
\\[4pt]
f_{121}
\\[4pt]
f_{158}
\\[4pt]
f_{109}
\\[4pt]
f_{107}
\\[4pt]
f_{151}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
f_{11101001}
\\[4pt]
f_{11010110}
\\[4pt]
f_{10110110}
\\[4pt]
f_{01111001}
\\[4pt]
f_{10011110}
\\[4pt]
f_{01101101}
\\[4pt]
f_{01101011}
\\[4pt]
f_{10010111}
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
1~1~1~0~1~0~0~1
\\[4pt]
1~1~0~1~0~1~1~0
\\[4pt]
1~0~1~1~0~1~1~0
\\[4pt]
0~1~1~1~1~0~0~1
\\[4pt]
1~0~0~1~1~1~1~0
\\[4pt]
0~1~1~0~1~1~0~1
\\[4pt]
0~1~1~0~1~0~1~1
\\[4pt]
1~0~0~1~0~1~1~1
\end{matrix}&lt;/math&gt;
|
&lt;math&gt;\begin{matrix}
\texttt{(((}p\texttt{),(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{(((}p\texttt{),}~q~\texttt{,}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,(}q\texttt{),}~r~\texttt{))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,(}r\texttt{)))}
\\[4pt]
\texttt{((}~p~\texttt{,}~q~\texttt{,}~r~\texttt{))}
\end{matrix}&lt;/math&gt;
|}

&lt;br&gt;

==Charts and graphs==

This Section focuses on visual representations of minimal negation operators.  A few bits of terminology are useful in describing the pictures, but the formal details are tedious reading, and may be familiar to many readers, so the full definitions of the terms marked in ''italics'' are relegated to a Glossary at the end of the article.

Two ways of visualizing the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; of &lt;math&gt;2^k&lt;/math&gt; points are the ''hypercube'' picture and the ''venn diagram'' picture.  The hypercube picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique point of the &lt;math&gt;k&lt;/math&gt;-dimensional hypercube.  The venn diagram picture associates each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; with a unique &amp;ldquo;cell&amp;rdquo; of the venn diagram on &lt;math&gt;k&lt;/math&gt; &amp;ldquo;circles&amp;rdquo;.

In addition, each point of &lt;math&gt;\mathbb{B}^k&lt;/math&gt; is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' &lt;math&gt;[|s|]&lt;/math&gt; of a ''singular proposition'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; and thus it is the unique point where a ''singular conjunction'' of &lt;math&gt;k&lt;/math&gt; ''literals'' is &lt;math&gt;1.&lt;/math&gt;

For example, consider two cases at opposite vertices of the cube:

{| align=&quot;center&quot; cellpadding=&quot;4&quot; width=&quot;90%&quot;
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(1, 1, \ldots , 1, 1)&lt;/math&gt; with all 1's as coordinates is the point where the conjunction of all posited variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;x_1 ~ x_2 ~\ldots~ x_{n-1} ~ x_n ~=~ 1.&lt;/math&gt;
|-
| valign=&quot;top&quot; | &lt;big&gt;&amp;bull;&lt;/big&gt;
| The point &lt;math&gt;(0, 0, \ldots , 0, 0)&lt;/math&gt; with all 0's as coordinates is the point where the conjunction of all negated variables evaluates to &lt;math&gt;1,&lt;/math&gt; namely, the point where:
|-
| &amp;nbsp;
| align=&quot;center&quot; | &lt;math&gt;\texttt{(} x_1 \texttt{)(} x_2 \texttt{)} \ldots \texttt{(} x_{n-1} \texttt{)(} x_n \texttt{)} ~=~ 1.&lt;/math&gt;
|}

To pass from these limiting examples to the general case, observe that a singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be given canonical expression as a conjunction of literals, &lt;math&gt;s = e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;.  Then the proposition &lt;math&gt;\nu (e_1, e_2, \ldots, e_{k-1}, e_k)&lt;/math&gt; is &lt;math&gt;1&lt;/math&gt; on the points adjacent to the point where &lt;math&gt;s&lt;/math&gt; is &lt;math&gt;1,&lt;/math&gt; and 0 everywhere else on the cube.

For example, consider the case where &lt;math&gt;k = 3.&lt;/math&gt;  Then the minimal negation operation &lt;math&gt;\nu (p, q, r)&lt;/math&gt; &amp;mdash; written more simply as &lt;math&gt;\texttt{(p, q, r)}&lt;/math&gt; &amp;mdash; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram (P,Q,R).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 4.}~~\texttt{(p, q, r)}&lt;/math&gt;&lt;/p&gt;
|}

For a contrasting example, the boolean function expressed by the form &lt;math&gt;\texttt{((p),(q),(r))}&lt;/math&gt; has the following venn diagram:

{| align=&quot;center&quot; cellpadding=&quot;8&quot; style=&quot;text-align:center&quot;
|
&lt;p&gt;[[File:Venn Diagram ((P),(Q),(R)).jpg|500px]]&lt;/p&gt;
&lt;p&gt;&lt;math&gt;\text{Figure 5.}~~\texttt{((p),(q),(r))}&lt;/math&gt;&lt;/p&gt;
|}

==Glossary of basic terms==

; Boolean domain
: A ''[[boolean domain]]'' &lt;math&gt;\mathbb{B}&lt;/math&gt; is a generic 2-element set, for example, &lt;math&gt;\mathbb{B} = \{ 0, 1 \},&lt;/math&gt; whose elements are interpreted as logical values, usually but not invariably with &lt;math&gt;0 = \mathrm{false}&lt;/math&gt; and &lt;math&gt;1 = \mathrm{true}.&lt;/math&gt;

; Boolean variable
: A ''boolean variable'' &lt;math&gt;x&lt;/math&gt; is a variable that takes its value from a boolean domain, as &lt;math&gt;x \in \mathbb{B}.&lt;/math&gt;

; Proposition
: In situations where boolean values are interpreted as logical values, a [[boolean-valued function]] &lt;math&gt;f : X \to \mathbb{B}&lt;/math&gt; or a [[boolean function]] &lt;math&gt;g : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is frequently called a ''proposition''.

; Basis element, Coordinate projection
: Given a sequence of &lt;math&gt;k&lt;/math&gt; boolean variables, &lt;math&gt;x_1, \ldots, x_k,&lt;/math&gt; each variable &lt;math&gt;x_j&lt;/math&gt; may be treated either as a ''basis element'' of the space &lt;math&gt;\mathbb{B}^k&lt;/math&gt; or as a ''coordinate projection'' &lt;math&gt;x_j : \mathbb{B}^k \to \mathbb{B}.&lt;/math&gt;

; Basic proposition
: This means that the set of objects &lt;math&gt;\{ x_j : 1 \le j \le k \}&lt;/math&gt; is a set of boolean functions &lt;math&gt;\{ x_j : \mathbb{B}^k \to \mathbb{B} \}&lt;/math&gt; subject to logical interpretation as a set of ''basic propositions'' that collectively generate the complete set of &lt;math&gt;2^{2^k}&lt;/math&gt; propositions over &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Literal
: A ''literal'' is one of the &lt;math&gt;2k&lt;/math&gt; propositions &lt;math&gt;x_1, \ldots, x_k, \texttt{(} x_1 \texttt{)}, \ldots, \texttt{(} x_k \texttt{)},&lt;/math&gt; in other words, either a ''posited'' basic proposition &lt;math&gt;x_j&lt;/math&gt; or a ''negated'' basic proposition &lt;math&gt;\texttt{(} x_j \texttt{)},&lt;/math&gt; for some &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

; Fiber
: In mathematics generally, the ''[[fiber (mathematics)|fiber]]'' of a point &lt;math&gt;y \in Y&lt;/math&gt; under a function &lt;math&gt;f : X \to Y&lt;/math&gt; is defined as the inverse image &lt;math&gt;f^{-1}(y) \subseteq X.&lt;/math&gt;

: In the case of a boolean function &lt;math&gt;f : \mathbb{B}^k \to \mathbb{B},&lt;/math&gt; there are just two fibers:
: The fiber of &lt;math&gt;0&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(0),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;0.&lt;/math&gt;
: The fiber of &lt;math&gt;1&lt;/math&gt; under &lt;math&gt;f,&lt;/math&gt; defined as &lt;math&gt;f^{-1}(1),&lt;/math&gt; is the set of points where the value of &lt;math&gt;f&lt;/math&gt; is &lt;math&gt;1.&lt;/math&gt;

; Fiber of truth
: When &lt;math&gt;1&lt;/math&gt; is interpreted as the logical value &lt;math&gt;\mathrm{true},&lt;/math&gt; then &lt;math&gt;f^{-1}(1)&lt;/math&gt; is called the ''fiber of truth'' in the proposition &lt;math&gt;f.&lt;/math&gt;  Frequent mention of this fiber makes it useful to have a shorter way of referring to it.  This leads to the definition of the notation &lt;math&gt;[|f|] = f^{-1}(1)&lt;/math&gt; for the fiber of truth in the proposition &lt;math&gt;f.&lt;/math&gt;

; Singular boolean function
: A ''singular boolean function'' &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a boolean function whose fiber of &lt;math&gt;1&lt;/math&gt; is a single point of &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular proposition
: In the interpretation where &lt;math&gt;1&lt;/math&gt; equals &lt;math&gt;\mathrm{true},&lt;/math&gt; a singular boolean function is called a ''singular proposition''.

: Singular boolean functions and singular propositions serve as functional or logical representatives of the points in &lt;math&gt;\mathbb{B}^k.&lt;/math&gt;

; Singular conjunction
: A ''singular conjunction'' in &lt;math&gt;\mathbb{B}^k \to \mathbb{B}&lt;/math&gt; is a conjunction of &lt;math&gt;k&lt;/math&gt; literals that includes just one conjunct of the pair &lt;math&gt;\{ x_j, ~\nu(x_j) \}&lt;/math&gt; for each &lt;math&gt;j = 1 ~\text{to}~ k.&lt;/math&gt;

: A singular proposition &lt;math&gt;s : \mathbb{B}^k \to \mathbb{B}&lt;/math&gt; can be expressed as a singular conjunction:

{| align=&quot;center&quot; cellspacing&quot;10&quot; width=&quot;90%&quot;
| height=&quot;36&quot; | &lt;math&gt;s ~=~ e_1 e_2 \ldots e_{k-1} e_k&lt;/math&gt;,
|-
|
&lt;math&gt;\begin{array}{llll}
\text{where} &amp; e_j &amp; = &amp; x_j
\\[6pt]
\text{or}    &amp; e_j &amp; = &amp; \nu (x_j),
\\[6pt]
\text{for}   &amp; j   &amp; = &amp; 1 ~\text{to}~ k.
\end{array}&lt;/math&gt;
|}

==Resources==

* [[Logic Syllabus]]

* [http://atlas.wolfram.com/ Wolfram Atlas of Simple Programs]
** [http://atlas.wolfram.com/01/01/ Elementary Cellular Automata Rules (ECARs)]
** [http://atlas.wolfram.com/01/01/rulelist.html ECAR Index]
** [http://atlas.wolfram.com/01/01/views/3/TableView.html ECAR Icons]
** [http://atlas.wolfram.com/01/01/views/87/TableView.html ECAR Examples]
** [http://atlas.wolfram.com/01/01/views/172/TableView.html ECAR Formulas]

[[Category:Automata theory]]
[[Category:Boolean algebra]]
[[Category:Boolean functions]]
[[Category:Combinatorics]]
[[Category:Computation theory]]
[[Category:Cybernetics]]
[[Category:Differential logic]]
[[Category:Discrete mathematics]]
[[Category:Equational inference]]
[[Category:Graph theory]]
[[Category:Logic]]
[[Category:Logical graphs]]
[[Category:Neural networks]]
[[Category:Peirce, Charles Sanders]]
[[Category:Propositional calculus]]
[[Category:Semiotics]]
[[Category:Set theory]]
[[Category:Visualization]]</text>
      <sha1>6fjhbukqx2ezwc90qxudg2fn9iq9wl9</sha1>
    </revision>
  </page>
  <page>
    <title>Python programming in plain view</title>
    <ns>0</ns>
    <id>212733</id>
    <revision>
      <id>2833723</id>
      <parentid>2833198</parentid>
      <timestamp>2026-09-18T08:10:09Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Using Libraries */</comment>
      <origin>2833723</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2696" sha1="9n60zuzc7wmbutw34b8bbl3pur1kwlc" xml:space="preserve">==''' Part I '''==
&lt;!----------------------------------------------------------------------&gt;
===  Introduction ===

* Overview 
* Memory 
* Number 

&lt;!----------------------------------------------------------------------&gt;


=== Python for C programmers ===

* Hello, World! ([[Media:CProg.Hello.1A.20230406.pdf |pdf]])
* Statement Level  ([[Media:CProg.Statement.1A.20230509.pdf |pdf]])
* Output with print
* Formatted output
* File IO

&lt;!----------------------------------------------------------------------&gt;


=== Using Libraries ===

* Scripts ([[Media:Python.Work2.Script.1A.20231129.pdf |pdf]])
* Modules ([[Media:Python.Work2.Module.1A.20231216.pdf |pdf]])
* Packages ([[Media:Python.Work2.Package.1A.20241207.pdf |pdf]])
* Libraries ([[Media:Python.Work2.Library.1A.20260915.pdf |A]], [[Media:Python.Work2.Library.1B.20260720.pdf |B]])
* Namespaces ([[Media:Python.Work2.Scope.1A.20231021.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

===   Handling Repetition ===
 
* Control ([[Media:Python.Repeat1.Control.1.A.20230314.pdf |pdf]])

* Loop ([[Media:Repeat2.Loop.1A.20230401.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling a Big Work ===

* Functions ([[Media:Python.Work1.Function.1A.20230529.pdf |pdf]])
* Lambda ([[Media:Python.Work2.Lambda.1A.20230705.pdf |pdf]])
* Type Annotations ([[Media:Python.Work2.AtypeAnnot.1A.20230817.pdf |pdf]])

  
&lt;!----------------------------------------------------------------------&gt;

=== Handling Series of Data ===

* Arrays ([[Media:Python.Series1.Array.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series2.Tuple.1A.pdf |pdf]])
* Lists ([[Media:Python.Series3.List.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series4.Tuple.1A.pdf |pdf]])
* Sets ([[Media:Python.Series5.Set.1A.pdf |pdf]])
* Dictionary ([[Media:Python.Series6.Dictionary.1A.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling Various Kinds of Data ===
  
* Types 
* Operators ([[Media:Python.Data3.Operators.1.A.pdf |pdf]])
* Files ([[Media:Python.Data4.File.1.A.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

=== Class and Objects ===
  
* Classes &amp; Objects ([[Media:Python.Work2.Class.1A.20230906.pdf |pdf]])
* Inheritance

 
&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;

== Python in Numerical Analysis  ==
 
&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

==External links==
* [http://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf Python and Computational Science and Engineering]</text>
      <sha1>9n60zuzc7wmbutw34b8bbl3pur1kwlc</sha1>
    </revision>
    <revision>
      <id>2833725</id>
      <parentid>2833723</parentid>
      <timestamp>2026-09-18T08:11:06Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Using Libraries */</comment>
      <origin>2833725</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2696" sha1="ds8h3txxr3mqp40rpor4saxfxdvf7lg" xml:space="preserve">==''' Part I '''==
&lt;!----------------------------------------------------------------------&gt;
===  Introduction ===

* Overview 
* Memory 
* Number 

&lt;!----------------------------------------------------------------------&gt;


=== Python for C programmers ===

* Hello, World! ([[Media:CProg.Hello.1A.20230406.pdf |pdf]])
* Statement Level  ([[Media:CProg.Statement.1A.20230509.pdf |pdf]])
* Output with print
* Formatted output
* File IO

&lt;!----------------------------------------------------------------------&gt;


=== Using Libraries ===

* Scripts ([[Media:Python.Work2.Script.1A.20231129.pdf |pdf]])
* Modules ([[Media:Python.Work2.Module.1A.20231216.pdf |pdf]])
* Packages ([[Media:Python.Work2.Package.1A.20241207.pdf |pdf]])
* Libraries ([[Media:Python.Work2.Library.1A.20260916.pdf |A]], [[Media:Python.Work2.Library.1B.20260720.pdf |B]])
* Namespaces ([[Media:Python.Work2.Scope.1A.20231021.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

===   Handling Repetition ===
 
* Control ([[Media:Python.Repeat1.Control.1.A.20230314.pdf |pdf]])

* Loop ([[Media:Repeat2.Loop.1A.20230401.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling a Big Work ===

* Functions ([[Media:Python.Work1.Function.1A.20230529.pdf |pdf]])
* Lambda ([[Media:Python.Work2.Lambda.1A.20230705.pdf |pdf]])
* Type Annotations ([[Media:Python.Work2.AtypeAnnot.1A.20230817.pdf |pdf]])

  
&lt;!----------------------------------------------------------------------&gt;

=== Handling Series of Data ===

* Arrays ([[Media:Python.Series1.Array.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series2.Tuple.1A.pdf |pdf]])
* Lists ([[Media:Python.Series3.List.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series4.Tuple.1A.pdf |pdf]])
* Sets ([[Media:Python.Series5.Set.1A.pdf |pdf]])
* Dictionary ([[Media:Python.Series6.Dictionary.1A.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling Various Kinds of Data ===
  
* Types 
* Operators ([[Media:Python.Data3.Operators.1.A.pdf |pdf]])
* Files ([[Media:Python.Data4.File.1.A.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

=== Class and Objects ===
  
* Classes &amp; Objects ([[Media:Python.Work2.Class.1A.20230906.pdf |pdf]])
* Inheritance

 
&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;

== Python in Numerical Analysis  ==
 
&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

==External links==
* [http://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf Python and Computational Science and Engineering]</text>
      <sha1>ds8h3txxr3mqp40rpor4saxfxdvf7lg</sha1>
    </revision>
    <revision>
      <id>2833727</id>
      <parentid>2833725</parentid>
      <timestamp>2026-09-18T08:11:55Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Using Libraries */</comment>
      <origin>2833727</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2696" sha1="qzwajgge8cejzun4rus2gxux1vykvky" xml:space="preserve">==''' Part I '''==
&lt;!----------------------------------------------------------------------&gt;
===  Introduction ===

* Overview 
* Memory 
* Number 

&lt;!----------------------------------------------------------------------&gt;


=== Python for C programmers ===

* Hello, World! ([[Media:CProg.Hello.1A.20230406.pdf |pdf]])
* Statement Level  ([[Media:CProg.Statement.1A.20230509.pdf |pdf]])
* Output with print
* Formatted output
* File IO

&lt;!----------------------------------------------------------------------&gt;


=== Using Libraries ===

* Scripts ([[Media:Python.Work2.Script.1A.20231129.pdf |pdf]])
* Modules ([[Media:Python.Work2.Module.1A.20231216.pdf |pdf]])
* Packages ([[Media:Python.Work2.Package.1A.20241207.pdf |pdf]])
* Libraries ([[Media:Python.Work2.Library.1A.20260917.pdf |A]], [[Media:Python.Work2.Library.1B.20260720.pdf |B]])
* Namespaces ([[Media:Python.Work2.Scope.1A.20231021.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

===   Handling Repetition ===
 
* Control ([[Media:Python.Repeat1.Control.1.A.20230314.pdf |pdf]])

* Loop ([[Media:Repeat2.Loop.1A.20230401.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling a Big Work ===

* Functions ([[Media:Python.Work1.Function.1A.20230529.pdf |pdf]])
* Lambda ([[Media:Python.Work2.Lambda.1A.20230705.pdf |pdf]])
* Type Annotations ([[Media:Python.Work2.AtypeAnnot.1A.20230817.pdf |pdf]])

  
&lt;!----------------------------------------------------------------------&gt;

=== Handling Series of Data ===

* Arrays ([[Media:Python.Series1.Array.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series2.Tuple.1A.pdf |pdf]])
* Lists ([[Media:Python.Series3.List.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series4.Tuple.1A.pdf |pdf]])
* Sets ([[Media:Python.Series5.Set.1A.pdf |pdf]])
* Dictionary ([[Media:Python.Series6.Dictionary.1A.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling Various Kinds of Data ===
  
* Types 
* Operators ([[Media:Python.Data3.Operators.1.A.pdf |pdf]])
* Files ([[Media:Python.Data4.File.1.A.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

=== Class and Objects ===
  
* Classes &amp; Objects ([[Media:Python.Work2.Class.1A.20230906.pdf |pdf]])
* Inheritance

 
&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;

== Python in Numerical Analysis  ==
 
&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

==External links==
* [http://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf Python and Computational Science and Engineering]</text>
      <sha1>qzwajgge8cejzun4rus2gxux1vykvky</sha1>
    </revision>
    <revision>
      <id>2833729</id>
      <parentid>2833727</parentid>
      <timestamp>2026-09-18T08:12:46Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Using Libraries */</comment>
      <origin>2833729</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2696" sha1="o4e9ozw31braws4km88mugu1rq3xz2r" xml:space="preserve">==''' Part I '''==
&lt;!----------------------------------------------------------------------&gt;
===  Introduction ===

* Overview 
* Memory 
* Number 

&lt;!----------------------------------------------------------------------&gt;


=== Python for C programmers ===

* Hello, World! ([[Media:CProg.Hello.1A.20230406.pdf |pdf]])
* Statement Level  ([[Media:CProg.Statement.1A.20230509.pdf |pdf]])
* Output with print
* Formatted output
* File IO

&lt;!----------------------------------------------------------------------&gt;


=== Using Libraries ===

* Scripts ([[Media:Python.Work2.Script.1A.20231129.pdf |pdf]])
* Modules ([[Media:Python.Work2.Module.1A.20231216.pdf |pdf]])
* Packages ([[Media:Python.Work2.Package.1A.20241207.pdf |pdf]])
* Libraries ([[Media:Python.Work2.Library.1A.20260918.pdf |A]], [[Media:Python.Work2.Library.1B.20260720.pdf |B]])
* Namespaces ([[Media:Python.Work2.Scope.1A.20231021.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

===   Handling Repetition ===
 
* Control ([[Media:Python.Repeat1.Control.1.A.20230314.pdf |pdf]])

* Loop ([[Media:Repeat2.Loop.1A.20230401.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling a Big Work ===

* Functions ([[Media:Python.Work1.Function.1A.20230529.pdf |pdf]])
* Lambda ([[Media:Python.Work2.Lambda.1A.20230705.pdf |pdf]])
* Type Annotations ([[Media:Python.Work2.AtypeAnnot.1A.20230817.pdf |pdf]])

  
&lt;!----------------------------------------------------------------------&gt;

=== Handling Series of Data ===

* Arrays ([[Media:Python.Series1.Array.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series2.Tuple.1A.pdf |pdf]])
* Lists ([[Media:Python.Series3.List.1A.pdf |pdf]])
* Tuples ([[Media:Python.Series4.Tuple.1A.pdf |pdf]])
* Sets ([[Media:Python.Series5.Set.1A.pdf |pdf]])
* Dictionary ([[Media:Python.Series6.Dictionary.1A.pdf |pdf]])

&lt;!----------------------------------------------------------------------&gt;

=== Handling Various Kinds of Data ===
  
* Types 
* Operators ([[Media:Python.Data3.Operators.1.A.pdf |pdf]])
* Files ([[Media:Python.Data4.File.1.A.pdf |pdf]])


&lt;!----------------------------------------------------------------------&gt;

=== Class and Objects ===
  
* Classes &amp; Objects ([[Media:Python.Work2.Class.1A.20230906.pdf |pdf]])
* Inheritance

 
&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;

== Python in Numerical Analysis  ==
 
&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

==External links==
* [http://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf Python and Computational Science and Engineering]</text>
      <sha1>o4e9ozw31braws4km88mugu1rq3xz2r</sha1>
    </revision>
  </page>
  <page>
    <title>Number bases</title>
    <ns>0</ns>
    <id>221875</id>
    <revision>
      <id>2833639</id>
      <parentid>2389141</parentid>
      <timestamp>2026-09-17T19:43:21Z</timestamp>
      <contributor>
        <username>~2026-50358-40</username>
        <id>3111209</id>
      </contributor>
      <origin>2833639</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="14301" sha1="pwv9eo53xcwde5nc94uw5sma8pam7ta" xml:space="preserve">Positive [[integers]] in decimal and in binary [[wikipedia:number base|bases]] of the ''n''-th [[wikipedia:power of two|power of two]] (2&lt;sup&gt;''n''&lt;/sup&gt;).

* [[wikipedia:base 10|decimal]]: base ten (10)
* [[wikipedia:base 2|binary]]: base two (2 = 2&lt;sup&gt;1&lt;/sup&gt;, first power of two)
* [[wikipedia:base 4|quaternary]]: base four (4 = 2&lt;sup&gt;2&lt;/sup&gt;, second power of two)
* [[wikipedia:base 8|octal]]: base eight (8 = 2&lt;sup&gt;3&lt;/sup&gt;, third power of two)
* [[wikipedia:base 16|hexadecimal]]: base sixteen (16 = 2&lt;sup&gt;4&lt;/sup&gt;, fourth power of two)
* [[wikipedia:base 32|duotrigesimal]]: base thirty-two (32 = 2&lt;sup&gt;5&lt;/sup&gt;, fifth power of two)
* [[wikipedia:base 64|tetrasexagesimal]]: base sixty-four (64 = 2&lt;sup&gt;6&lt;/sup&gt;, sixth power of two)
* centoctovigesimal: base 128 = 2&lt;sup&gt;7&lt;/sup&gt; (seventh power of two)
* ducentohexaquinquagesimal: base 256 = 2&lt;sup&gt;8&lt;/sup&gt; (eighth power of two)
* quingentoduodecimal: base 512 = 2&lt;sup&gt;9&lt;/sup&gt; (ninth power of two)
* milletetravigesimal: base 1,024 = 2&lt;sup&gt;10&lt;/sup&gt; (tenth power of two)
* dumilloctoquadragesimal: base 2,048 = 2&lt;sup&gt;11&lt;/sup&gt; (eleventh power of two)
* quadramillehexanonagesimal: base 4,096 = 2&lt;sup&gt;12&lt;/sup&gt; (twelfth power of two)

Note that bases 63 and higher include arbitrary characters for numerals (since the number of Hindu-Arabic numerals, plus Roman uppercase and Roman lowercase letters, equals 62 characters).  Base 64 is presented here using the additional two characters of &quot;-&quot; (hyphen) and &quot;_&quot; (underscore) from the &quot;[[wikipedia:Base64#Variants summary table|URL- and Filename-Safe Base-64 Alphabet]]&quot; of Internet Engineering Task Force (IETF) [[wikipedia:Request for Comments|RFC]] 4648.

{| class=&quot;wikitable sortable&quot;
! base 10
! base 2
! base 4
! base 8
! base 16
! base 32
! base 64
|- 
| 0
| 0
| 0
| 0
| 0
| 0
| 0
|- 
| 1
| 1
| 1
| 1
| 1
| 1
| 1
|- 
| 2
| 10
| 2
| 2
| 2
| 2
| 2
|- 
| 3
| 11
| 3
| 3
| 3
| 3
| 3
|- 
| 4
| 100
| 10
| 4
| 4
| 4
| 4
|- 
| 5
| 101
| 11
| 5
| 5
| 5
| 5
|- 
| 6
| 110
| 12
| 6
| 6
| 6
| 6
|- 
| 7
| 111
| 13
| 7
| 7
| 7
| 7
|- 
| 8
| 1000
| 20
| 10
| 8
| 8
| 8
|- 
| 9
| 1001
| 21
| 11
| 9
| 9
| 9
|- 
| 10
| 1010
| 22
| 12
| A
| A
| A
|- 
| 11
| 1011
| 23
| 13
| B
| B
| B
|- 
| 12
| 1100
| 30
| 14
| C
| C
| C
|- 
| 13
| 1101
| 31
| 15
| D
| D
| D
|- 
| 14
| 1110
| 32
| 16
| E
| E
| E
|- 
| 15
| 1111
| 33
| 17
| F
| F
| F
|- 
| 16
| 10000
| 100
| 20
| 10
| G
| G
|- 
| 17
| 10001
| 101
| 21
| 11
| H
| H
|- 
| 18
| 10010
| 102
| 22
| 12
| I
| I
|- 
| 19
| 10011
| 103
| 23
| 13
| J
| J
|- 
| 20
| 10100
| 110
| 24
| 14
| K
| K
|- 
| 21
| 10101
| 111
| 25
| 15
| L
| L
|- 
| 22
| 10110
| 112
| 26
| 16
| M
| M
|- 
| 23
| 10111
| 113
| 27
| 17
| N
| N
|- 
| 24
| 11000
| 120
| 30
| 18
| O
| O
|- 
| 25
| 11001
| 121
| 31
| 19
| P
| P
|- 
| 26
| 11010
| 122
| 32
| 1A
| Q
| Q
|- 
| 27
| 11011
| 123
| 33
| 1B
| R
| R
|- 
| 28
| 11100
| 130
| 34
| 1C
| S
| S
|- 
| 29
| 11101
| 131
| 35
| 1D
| T
| T
|- 
| 30
| 11110
| 132
| 36
| 1E
| U
| U
|- 
| 31
| 11111
| 133
| 37
| 1F
| V
| V
|- 
| 32
| 100000
| 200
| 40
| 20
| 10
| W
|- 
| 33
| 100001
| 201
| 41
| 21
| 11
| X
|- 
| 34
| 100010
| 202
| 42
| 22
| 12
| Y
|- 
| 35
| 100011
| 203
| 43
| 23
| 13
| Z
|- 
| 36
| 100100
| 210
| 44
| 24
| 14
| a
|- 
| 37
| 100101
| 211
| 45
| 25
| 15
| b
|- 
| 38
| 100110
| 212
| 46
| 26
| 16
| c
|- 
| 39
| 100111
| 213
| 47
| 27
| 17
| d
|- 
| 40
| 101000
| 220
| 50
| 28
| 18
| e
|- 
| 41
| 101001
| 221
| 51
| 29
| 19
| f
|- 
| 42
| 101010
| 222
| 52
| 2A
| 1A
| g
|- 
| 43
| 101011
| 223
| 53
| 2B
| 1B
| h
|- 
| 44
| 101100
| 230
| 54
| 2C
| 1C
| i
|- 
| 45
| 101101
| 231
| 55
| 2D
| 1D
| j
|- 
| 46
| 101110
| 232
| 56
| 2E
| 1E
| k
|- 
| 47
| 101111
| 233
| 57
| 2F
| 1F
| l
|- 
| 48
| 110000
| 300
| 60
| 30
| 1G
| m
|- 
| 49
| 110001
| 301
| 61
| 31
| 1H
| n
|- 
| 50
| 110010
| 302
| 62
| 32
| 1I
| o
|- 
| 51
| 110011
| 303
| 63
| 33
| 1J
| p
|- 
| 52
| 110100
| 310
| 64
| 34
| 1K
| q
|- 
| 53
| 110101
| 311
| 65
| 35
| 1L
| r
|- 
| 54
| 110110
| 312
| 66
| 36
| 1M
| s
|- 
| 55
| 110111
| 313
| 67
| 37
| 1N
| t
|- 
| 56
| 111000
| 320
| 70
| 38
| 1O
| u
|- 
| 57
| 111001
| 321
| 71
| 39
| 1P
| v
|- 
| 58
| 111010
| 322
| 72
| 3A
| 1Q
| w
|- 
| 59
| 111011
| 323
| 73
| 3B
| 1R
| x
|- 
| 60
| 111100
| 330
| 74
| 3C
| 1S
| y
|- 
| 61
| 111101
| 331
| 75
| 3D
| 1T
| z
|- 
| 62
| 111110
| 332
| 76
| 3E
| 1U
| -
|- 
| 63
| 111111
| 333
| 77
| 3F
| 1V
| _
|- 
| 64
| 1000000
| 1000
| 100
| 40
| 20
| 10
|- 
| 65
| 1000001
| 1001
| 101
| 41
| 21
| 11
|- 
| 66
| 1000010
| 1002
| 102
| 42
| 22
| 12
|- 
| 67
| 1000011
| 1003
| 103
| 43
| 23
| 13
|- 
| 68
| 1000100
| 1010
| 104
| 44
| 24
| 14
|- 
| 69
| 1000101
| 1011
| 105
| 45
| 25
| 15
|- 
| 70
| 1000110
| 1012
| 106
| 46
| 26
| 16
|- 
| 71
| 1000111
| 1013
| 107
| 47
| 27
| 17
|- 
| 72
| 1001000
| 1020
| 110
| 48
| 28
| 18
|- 
| 73
| 1001001
| 1021
| 111
| 49
| 29
| 19
|- 
| 74
| 1001010
| 1022
| 112
| 4A
| 2A
| 1A
|- 
| 75
| 1001011
| 1023
| 113
| 4B
| 2B
| 1B
|- 
| 76
| 1001100
| 1030
| 114
| 4C
| 2C
| 1C
|- 
| 77
| 1001101
| 1031
| 115
| 4D
| 2D
| 1D
|- 
| 78
| 1001110
| 1032
| 116
| 4E
| 2E
| 1E
|- 
| 79
| 1001111
| 1033
| 117
| 4F
| 2F
| 1F
|- 
| 80
| 1010000
| 1100
| 120
| 50
| 2G
| 1G
|- 
| 81
| 1010001
| 1101
| 121
| 51
| 2H
| 1H
|- 
| 82
| 1010010
| 1102
| 122
| 52
| 2I
| 1I
|- 
| 83
| 1010011
| 1103
| 123
| 53
| 2J
| 1J
|- 
| 84
| 1010100
| 1110
| 124
| 54
| 2K
| 1K
|- 
| 85
| 1010101
| 1111
| 125
| 55
| 2L
| 1L
|- 
| 86
| 1010110
| 1112
| 126
| 56
| 2M
| 1M
|- 
| 87
| 1010111
| 1113
| 127
| 57
| 2N
| 1N
|- 
| 88
| 1011000
| 1120
| 130
| 58
| 2O
| 1O
|- 
| 89
| 1011001
| 1121
| 131
| 59
| 2P
| 1P
|- 
| 90
| 1011010
| 1122
| 132
| 5A
| 2Q
| 1Q
|- 
| 91
| 1011011
| 1123
| 133
| 5B
| 2R
| 1R
|- 
| 92
| 1011100
| 1130
| 134
| 5C
| 2S
| 1S
|- 
| 93
| 1011101
| 1131
| 135
| 5D
| 2T
| 1T
|- 
| 94
| 1011110
| 1132
| 136
| 5E
| 2U
| 1U
|- 
| 95
| 1011111
| 1133
| 137
| 5F
| 2V
| 1V
|- 
| 96
| 1100000
| 1200
| 140
| 60
| 30
| 1W
|- 
| 97
| 1100001
| 1201
| 141
| 61
| 31
| 1X
|- 
| 98
| 1100010
| 1202
| 142
| 62
| 32
| 1Y
|- 
| 99
| 1100011
| 1203
| 143
| 63
| 33
| 1Z
|- 
| 100
| 1100100
| 1210
| 144
| 64
| 34
| 1a
|- 
| 101
| 1100101
| 1211
| 145
| 65
| 35
| 1b
|- 
| 102
| 1100110
| 1212
| 146
| 66
| 36
| 1c
|- 
| 103
| 1100111
| 1213
| 147
| 67
| 37
| 1d
|- 
| 104
| 1101000
| 1220
| 150
| 68
| 38
| 1e
|- 
| 105
| 1101001
| 1221
| 151
| 69
| 39
| 1f
|- 
| 106
| 1101010
| 1222
| 152
| 6A
| 3A
| 1g
|- 
| 107
| 1101011
| 1223
| 153
| 6B
| 3B
| 1h
|- 
| 108
| 1101100
| 1230
| 154
| 6C
| 3C
| 1i
|- 
| 109
| 1101101
| 1231
| 155
| 6D
| 3D
| 1j
|- 
| 110
| 1101110
| 1232
| 156
| 6E
| 3E
| 1k
|- 
| 111
| 1101111
| 1233
| 157
| 6F
| 3F
| 1l
|- 
| 112
| 1110000
| 1300
| 160
| 70
| 3G
| 1m
|- 
| 113
| 1110001
| 1301
| 161
| 71
| 3H
| 1n
|- 
| 114
| 1110010
| 1302
| 162
| 72
| 3I
| 1o
|- 
| 115
| 1110011
| 1303
| 163
| 73
| 3J
| 1p
|- 
| 116
| 1110100
| 1310
| 164
| 74
| 3K
| 1q
|- 
| 117
| 1110101
| 1311
| 165
| 75
| 3L
| 1r
|- 
| 118
| 1110110
| 1312
| 166
| 76
| 3M
| 1s
|- 
| 119
| 1110111
| 1313
| 167
| 77
| 3N
| 1t
|- 
| 120
| 1111000
| 1320
| 170
| 78
| 3O
| 1u
|- 
| 121
| 1111001
| 1321
| 171
| 79
| 3P
| 1v
|- 
| 122
| 1111010
| 1322
| 172
| 7A
| 3Q
| 1w
|- 
| 123
| 1111011
| 1323
| 173
| 7B
| 3R
| 1x
|- 
| 124
| 1111100
| 1330
| 174
| 7C
| 3S
| 1y
|- 
| 125
| 1111101
| 1331
| 175
| 7D
| 3T
| 1z
|- 
| 126
| 1111110
| 1332
| 176
| 7E
| 3U
| 1-
|- 
| 127
| 1111111
| 1333
| 177
| 7F
| 3V
| 1_
|- 
| 128
| 10000000
| 2000
| 200
| 80
| 40
| 20
|- 
| 129
| 10000001
| 2001
| 201
| 81
| 41
| 21
|- 
| 130
| 10000010
| 2002
| 202
| 82
| 42
| 22
|- 
| 131
| 10000011
| 2003
| 203
| 83
| 43
| 23
|- 
| 132
| 10000100
| 2010
| 204
| 84
| 44
| 24
|- 
| 133
| 10000101
| 2011
| 205
| 85
| 45
| 25
|- 
| 134
| 10000110
| 2012
| 206
| 86
| 46
| 26
|- 
| 135
| 10000111
| 2013
| 207
| 87
| 47
| 27
|- 
| 136
| 10001000
| 2020
| 210
| 88
| 48
| 28
|- 
| 137
| 10001001
| 2021
| 211
| 89
| 49
| 29
|- 
| 138
| 10001010
| 2022
| 212
| 8A
| 4A
| 2A
|- 
| 139
| 10001011
| 2023
| 213
| 8B
| 4B
| 2B
|- 
| 140
| 10001100
| 2030
| 214
| 8C
| 4C
| 2C
|- 
| 141
| 10001101
| 2031
| 215
| 8D
| 4D
| 2D
|- 
| 142
| 10001110
| 2032
| 216
| 8E
| 4E
| 2E
|- 
| 143
| 10001111
| 2033
| 217
| 8F
| 4F
| 2F
|- 
| 144
| 10010000
| 2100
| 220
| 90
| 4G
| 2G
|- 
| 145
| 10010001
| 2101
| 221
| 91
| 4H
| 2H
|- 
| 146
| 10010010
| 2102
| 222
| 92
| 4I
| 2I
|- 
| 147
| 10010011
| 2103
| 223
| 93
| 4J
| 2J
|- 
| 148
| 10010100
| 2110
| 224
| 94
| 4K
| 2K
|- 
| 149
| 10010101
| 2111
| 225
| 95
| 4L
| 2L
|- 
| 150
| 10010110
| 2112
| 226
| 96
| 4M
| 2M
|- 
| 151
| 10010111
| 2113
| 227
| 97
| 4N
| 2N
|- 
| 152
| 10011000
| 2120
| 230
| 98
| 4O
| 2O
|- 
| 153
| 10011001
| 2121
| 231
| 99
| 4P
| 2P
|- 
| 154
| 10011010
| 2122
| 232
| 9A
| 4Q
| 2Q
|- 
| 155
| 10011011
| 2123
| 233
| 9B
| 4R
| 2R
|- 
| 156
| 10011100
| 2130
| 234
| 9C
| 4S
| 2S
|- 
| 157
| 10011101
| 2131
| 235
| 9D
| 4T
| 2T
|- 
| 158
| 10011110
| 2132
| 236
| 9E
| 4U
| 2U
|- 
| 159
| 10011111
| 2133
| 237
| 9F
| 4V
| 2V
|- 
| 160
| 10100000
| 2200
| 240
| A0
| 50
| 2W
|- 
| 161
| 10100001
| 2201
| 241
| A1
| 51
| 2X
|- 
| 162
| 10100010
| 2202
| 242
| A2
| 52
| 2Y
|- 
| 163
| 10100011
| 2203
| 243
| A3
| 53
| 2Z
|- 
| 164
| 10100100
| 2210
| 244
| A4
| 54
| 2a
|- 
| 165
| 10100101
| 2211
| 245
| A5
| 55
| 2b
|- 
| 166
| 10100110
| 2212
| 246
| A6
| 56
| 2c
|- 
| 167
| 10100111
| 2213
| 247
| A7
| 57
| 2d
|- 
| 168
| 10101000
| 2220
| 250
| A8
| 58
| 2e
|- 
| 169
| 10101001
| 2221
| 251
| A9
| 59
| 2f
|- 
| 170
| 10101010
| 2222
| 252
| AA
| 5A
| 2g
|- 
| 171
| 10101011
| 2223
| 253
| AB
| 5B
| 2h
|- 
| 172
| 10101100
| 2230
| 254
| AC
| 5C
| 2i
|- 
| 173
| 10101101
| 2231
| 255
| AD
| 5D
| 2j
|- 
| 174
| 10101110
| 2232
| 256
| AE
| 5E
| 2k
|- 
| 175
| 10101111
| 2233
| 257
| AF
| 5F
| 2l
|- 
| 176
| 10110000
| 2300
| 260
| B0
| 5G
| 2m
|- 
| 177
| 10110001
| 2301
| 261
| B1
| 5H
| 2n
|- 
| 178
| 10110010
| 2302
| 262
| B2
| 5I
| 2o
|- 
| 179
| 10110011
| 2303
| 263
| B3
| 5J
| 2p
|- 
| 180
| 10110100
| 2310
| 264
| B4
| 5K
| 2q
|- 
| 181
| 10110101
| 2311
| 265
| B5
| 5L
| 2r
|- 
| 182
| 10110110
| 2312
| 266
| B6
| 5M
| 2s
|- 
| 183
| 10110111
| 2313
| 267
| B7
| 5N
| 2t
|- 
| 184
| 10111000
| 2320
| 270
| B8
| 5O
| 2u
|- 
| 185
| 10111001
| 2321
| 271
| B9
| 5P
| 2v
|- 
| 186
| 10111010
| 2322
| 272
| BA
| 5Q
| 2w
|- 
| 187
| 10111011
| 2323
| 273
| BB
| 5R
| 2x
|- 
| 188
| 10111100
| 2330
| 274
| BC
| 5S
| 2y
|- 
| 189
| 10111101
| 2331
| 275
| BD
| 5T
| 2z
|- 
| 190
| 10111110
| 2332
| 276
| BE
| 5U
| 2-
|- 
| 191
| 10111111
| 2333
| 277
| BF
| 5V
| 2_
|- 
| 192
| 11000000
| 3000
| 300
| C0
| 60
| 30
|- 
| 193
| 11000001
| 3001
| 301
| C1
| 61
| 31
|- 
| 194
| 11000010
| 3002
| 302
| C2
| 62
| 32
|- 
| 195
| 11000011
| 3003
| 303
| C3
| 63
| 33
|- 
| 196
| 11000100
| 3010
| 304
| C4
| 64
| 34
|- 
| 197
| 11000101
| 3011
| 305
| C5
| 65
| 35
|- 
| 198
| 11000110
| 3012
| 306
| C6
| 66
|36
|- 
| 199
| 11000111
| 3013
| 307
| C7
| 67
| 37
|- 
| 200
| 11001000
| 3020
| 310
| C8
| 68
| 38
|- 
| 201
| 11001001
| 3021
| 311
| C9
| 69
| 39
|- 
| 202
| 11001010
| 3022
| 312
| CA
| 6A
| 3A
|- 
| 203
| 11001011
| 3023
| 313
| CB
| 6B
| 3B
|- 
| 204
| 11001100
| 3030
| 314
| CC
| 6C
| 3C
|- 
| 205
| 11001101
| 3031
| 315
| CD
| 6D
| 3D
|- 
| 206
| 11001110
| 3032
| 316
| CE
| 6E
| 3E
|- 
| 207
| 11001111
| 3033
| 317
| CF
| 6F
| 3F
|- 
| 208
| 11010000
| 3100
| 320
| D0
| 6G
| 3G
|- 
| 209
| 11010001
| 3101
| 321
| D1
| 6H
| 3H
|- 
| 210
| 11010010
| 3102
| 322
| D2
| 6I
| 3I
|- 
| 211
| 11010011
| 3103
| 323
| D3
| 6J
| 3J
|- 
| 212
| 11010100
| 3110
| 324
| D4
| 6K
| 3K
|- 
| 213
| 11010101
| 3111
| 325
| D5
| 6L
| 3L
|- 
| 214
| 11010110
| 3112
| 326
| D6
| 6M
| 3M
|- 
| 215
| 11010111
| 3113
| 327
| D7
| 6N
| 3N
|- 
| 216
| 11011000
| 3120
| 330
| D8
| 6O
| 3O
|- 
| 217
| 11011001
| 3121
| 331
| D9
| 6P
| 3P
|- 
| 218
| 11011010
| 3122
| 332
| DA
| 6Q
| 3Q
|- 
| 219
| 11011011
| 3123
| 333
| DB
| 6R
| 3R
|- 
| 220
| 11011100
| 3130
| 334
| DC
| 6S
| 3S
|- 
| 221
| 11011101
| 3131
| 335
| DD
| 6T
| 3T
|- 
| 222
| 11011110
| 3132
| 336
| DE
| 6U
| 3U
|- 
| 223
| 11011111
| 3133
| 337
| DF
| 6V
| 3V
|- 
| 224
| 11100000
| 3200
| 340
| E0
| 70
| 3W
|- 
| 225
| 11100001
| 3201
| 341
| E1
| 71
| 3X
|- 
| 226
| 11100010
| 3202
| 342
| E2
| 72
| 3Y
|- 
| 227
| 11100011
| 3203
| 343
| E3
| 73
| 3Z
|- 
| 228
| 11100100
| 3210
| 344
| E4
| 74
| 3a
|- 
| 229
| 11100101
| 3211
| 345
| E5
| 75
| 3b
|- 
| 230
| 11100110
| 3212
| 346
| E6
| 76
| 3c
|- 
| 231
| 11100111
| 3213
| 347
| E7
| 77
| 3d
|- 
| 232
| 11101000
| 3220
| 350
| E8
| 78
| 3e
|- 
| 233
| 11101001
| 3221
| 351
| E9
| 79
| 3f
|- 
| 234
| 11101010
| 3222
| 352
| EA
| 7A
| 3g
|- 
| 235
| 11101011
| 3223
| 353
| EB
| 7B
| 3h
|- 
| 236
| 11101100
| 3230
| 354
| EC
| 7C
| 3i
|- 
| 237
| 11101101
| 3231
| 355
| ED
| 7D
| 3j
|- 
| 238
| 11101110
| 3232
| 356
| EE
| 7E
| 3k
|- 
| 239
| 11101111
| 3233
| 357
| EF
| 7F
| 3l
|- 
| 240
| 11110000
| 3300
| 360
| F0
| 7G
| 3m
|- 
| 241
| 11110001
| 3301
| 361
| F1
| 7H
| 3n
|- 
| 242
| 11110010
| 3302
| 362
| F2
| 7I
| 3o
|- 
| 243
| 11110011
| 3303
| 363
| F3
| 7J
| 3p
|- 
| 244
| 11110100
| 3310
| 364
| F4
| 7K
| 3q
|- 
| 245
| 11110101
| 3311
| 365
| F5
| 7L
| 3r
|- 
| 246
| 11110110
| 3312
| 366
| F6
| 7M
| 3s
|- 
| 247
| 11110111
| 3313
| 367
| F7
| 7N
| 3t
|- 
| 248
| 11111000
| 3320
| 370
| F8
| 7O
| 3u
|- 
| 249
| 11111001
| 3321
| 371
| F9
| 7P
| 3v
|- 
| 250
| 11111010
| 3322
| 372
| FA
| 7Q
| 3w
|- 
| 251
| 11111011
| 3323
| 373
| FB
| 7R
| 3x
|- 
| 252
| 11111100
| 3330
| 374
| FC
| 7S
| 3y
|- 
| 253
| 11111101
| 3331
| 375
| FD
| 7T
| 3z
|- 
| 254
| 11111110
| 3332
| 376
| FE
| 7U
| 3-
|- 
| 255
| 11111111
| 3333
| 377
| FF
| 7V
| 3_
|- 
| 256
| 100000000
| 10000
| 400
| 100
| 80
| 40
|}

== Additional Resources ==

* [[Number bases/Introduction]]
* [[wikipedia:list of numeral systems|Wikipedia's List of Numeral Systems]] 
* [[wiktionary:Appendix:Number bases|Wiktionary Appendex on Names for Number Bases]]
* [http://www.mathforum.org/library/drmath/view/60405.html Names of Bases on The Math Forum]
* [http://www.numberbases.com/terms/basename.html Names of Number Bases by a &quot;Radicologist&quot;]
* [http://www.minus40.info/sky/binaryoctalhexdec.html Conversion List for Binary, Octal, and Hexadecimal Numbers]
* [[wikipedia:table of bases|Table of Bases on Wikipedia]]</text>
      <sha1>pwv9eo53xcwde5nc94uw5sma8pam7ta</sha1>
    </revision>
  </page>
  <page>
    <title>Sitemaps</title>
    <ns>0</ns>
    <id>233641</id>
    <revision>
      <id>2833733</id>
      <parentid>2624325</parentid>
      <timestamp>2026-09-18T08:49:00Z</timestamp>
      <contributor>
        <username>~2026-50448-11</username>
        <id>3111229</id>
      </contributor>
      <comment>/* external links */</comment>
      <origin>2833733</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2589" sha1="2lyk52qnt2xihak326folnmoo95w8rf" xml:space="preserve">A [[wikipedia:sitemap|sitemap]] is a good way to help searchbots index your website, and increase your search-engine rankings.

== plaintext sitemaps ==

The easiest way to create a sitemap (for a small website) is to simply list out each webpage on your site in a plaintext file, with one [[wikipedia:URL|URL]] per line, saved as &quot;&lt;code&gt;sitemap.txt&lt;/code&gt;&quot; in your website's root directory.

=== example plaintext sitemap ===

The plaintext below, if saved in [[wikipedia:UTF-8|UTF-8]] as &quot;&lt;code&gt;sitemap.txt&lt;/code&gt;&quot; and placed in the root directory at &quot;&lt;code&gt;&lt;nowiki&gt;https://en.wikiversity.org/sitemap.txt&lt;/nowiki&gt;&lt;/code&gt;,&quot; would help searchbots to index those links and pages for their search engines.

&lt;pre&gt;
https://en.wikiversity.org/
https://en.wikiversity.org/w/
https://en.wikiversity.org/wiki/
https://en.wikiversity.org/wiki/Main_Page
https://en.wikiversity.org/wiki/sitemap
https://en.wikiversity.org/wiki/Sitemaps
&lt;/pre&gt;

=== notes ===

* Always place your sitemap in the website's root directory if possible.
* Always save a sitemap as UTF-8.
* Do not list more than one URL per line.
* Do not add any additional text or comments.
* Do not list more than one host or subdomain, e.g. URLs for &quot;&lt;code&gt;https://www.wikiversity.org/&lt;/code&gt;&quot; or &quot;&lt;code&gt;https://de.wikiversity.org/&lt;/code&gt;&quot; should not be listed on the sitemap for &quot;&lt;code&gt;https://en.wikiversity.org/&lt;/code&gt;.&quot;  Each host or subdomain will need its own sitemap.
* Do not list URLs using more than one protocol.  All of the URLs listed should be either just HTTP or just HTTPS.
* Do not list more than 50,000 URLs.
* The total size of the text file must be less than 50 megabytes.

== XML sitemaps ==

Sitemaps can also be encoded in [[wikipedia:XML|XML]], and saved as &quot;&lt;code&gt;sitemap.xml&lt;/code&gt;&quot; in the root directory.

=== example XML sitemap ===

&lt;source lang=&quot;xml&quot;&gt;
&lt;?xml version=&quot;1.0&quot; encoding=&quot;UTF-8&quot;?&gt;
&lt;urlset xmlns=&quot;http://www.sitemaps.org/schemas/sitemap/0.9&quot;&gt;
  &lt;url&gt;
    &lt;loc&gt;http://www.example.net/?id=who&lt;/loc&gt;
    &lt;lastmod&gt;2009-09-22&lt;/lastmod&gt;
    &lt;changefreq&gt;monthly&lt;/changefreq&gt;
    &lt;priority&gt;0.8&lt;/priority&gt;
  &lt;/url&gt;
  &lt;url&gt;
    &lt;loc&gt;http://www.example.net/?id=what&lt;/loc&gt;
    &lt;lastmod&gt;2009-09-22&lt;/lastmod&gt;
    &lt;changefreq&gt;monthly&lt;/changefreq&gt;
    &lt;priority&gt;0.5&lt;/priority&gt;
  &lt;/url&gt;
  &lt;url&gt;
    &lt;loc&gt;http://www.example.net/?id=how&lt;/loc&gt;
    &lt;lastmod&gt;2009-09-22&lt;/lastmod&gt;
    &lt;changefreq&gt;monthly&lt;/changefreq&gt;
    &lt;priority&gt;0.5&lt;/priority&gt;
  &lt;/url&gt;
&lt;/urlset&gt;
&lt;/source&gt;

== external links ==

* https://www.sitemaps.org/
* https://seotesting.com/free-seo-tools/xml-sitemap-generator/

[[category:web development]]</text>
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    </revision>
  </page>
  <page>
    <title>Talk:Plant Divisions (Phyla)</title>
    <ns>1</ns>
    <id>235273</id>
    <revision>
      <id>2833646</id>
      <parentid>1859972</parentid>
      <timestamp>2026-09-17T21:00:30Z</timestamp>
      <contributor>
        <username>The Citer</username>
        <id>3110681</id>
      </contributor>
      <comment>/* */ Reply</comment>
      <origin>2833646</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="376" sha1="1qqsqhcchd7hj4xdi2cu1s1vafqr42h" xml:space="preserve">created as a companion piece to [[Animal Phyla]] as a resource on biological diversity.--[[User:Rhole2001|Rhole2001]] ([[User talk:Rhole2001|discuss]] • [[Special:Contributions/Rhole2001|contribs]]) 06:28, 27 April 2018 (UTC)

:Ok. [[User:The Citer|The Citer]] ([[User talk:The Citer|discuss]] • [[Special:Contributions/The Citer|contribs]]) 21:00, 17 September 2026 (UTC)</text>
      <sha1>1qqsqhcchd7hj4xdi2cu1s1vafqr42h</sha1>
    </revision>
  </page>
  <page>
    <title>Social Victorians/Timeline/1890</title>
    <ns>0</ns>
    <id>264277</id>
    <revision>
      <id>2833648</id>
      <parentid>2833542</parentid>
      <timestamp>2026-09-17T22:35:05Z</timestamp>
      <contributor>
        <username>Scogdill</username>
        <id>1331941</id>
      </contributor>
      <comment>/* February 1890 */</comment>
      <origin>2833648</origin>
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      <text bytes="110544" sha1="e7exydul7xm74s8rvxd6l9cs0pcwwk5" xml:space="preserve">[[Social Victorians/Timeline/1840s|1840s]]  [[Social Victorians/Timeline/1850s |1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s Headlines]] [[Social Victorians/Timeline/1890s | 1890s Headlines]] 1890 [[Social Victorians/Timeline/1891 | 1891]] [[Social Victorians/Timeline/1892 | 1892]] [[Social Victorians/Timeline/1893 | 1893]] [[Social Victorians/Timeline/1894 | 1894]] [[Social Victorians/Timeline/1895 | 1895]] [[Social Victorians/Timeline/1896 | 1896]] [[Social Victorians/Timeline/1897 | 1897]] [[Social Victorians/Timeline/1898 | 1898]] [[Social Victorians/Timeline/1899 | 1899]]  [[Social Victorians/Timeline/1900s|1900s]] [[Social Victorians/Timeline/1910s|1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]]

==January 1890==
Sometime in January 1890, [[Social Victorians/People/Horniman|Annie Horniman]] was initiated into the Golden Dawn (Gilbert 86 144).

Sometime in 1890 Annie Besant and [[Social Victorians/People/Helena Blavatsky|Helena Blavatsky]] founded the Working Women's Club in the East End (Besant Chronology.pdf). Maye Dilke was a member (Crawford 170).

[[Social Victorians/People/Frank Harris|Frank Harris]] says,&lt;blockquote&gt;One day in 1890 I had George Meredith, Walter Pater and [[Social Victorians/People/Oscar Wilde|Oscar Wilde]] dining with me in Park Lane and the time of sex-awakening was discussed. Both Pater and Wilde spoke of it as a sign of puberty. Pater thought it began about thirteen or fourteen and Wilde to my amazement set it as late as sixteen. Meredith alone was inclined to put it earlier.&lt;ref&gt;Harris, Frank. ''My Life and Loves''.&lt;/ref&gt;&lt;/blockquote&gt;

===1 January 1890, Wednesday, New Year's Day===
&lt;blockquote&gt;Sharp frost was experienced over the East of England yesterday morning, and in South London the thermometer had been as low as 27deg., and 28deg. in Hyde-park. It rose during the day to 41deg., but in the evening frost again set in. Later the thermometer rose again to 32deg., and there was an appearance as of coming rain.&lt;ref&gt;&lt;cite&gt;The Morning Post. 1 January 1890 (No. 36,675): P. 4, Col. F.&lt;/cite&gt;&lt;/ref&gt;&lt;/blockquote&gt;Influenza is spreading all over Europe.

According to the &quot;Court Circular: Orders for Court Mourning&quot; in the Morning Post,&lt;blockquote&gt;A second supplement to the Gazette, issued last night, contains the following: —

&quot;Lord Chamberlain's Office, January 1.

&quot;Orders for the Court's going into mourning on Thursday next, the 2d instant, for her late Majesty the Empress of Brazil, viz.&quot; —

&quot;The ladies to wear black dresses, white gloves, black or white shoes, feathers, and fans, pearls, diamonds, or plain gold or silver ornaments. The gentlemen to wear black Court dress, with black swords and buckles.

&quot;The Court to change the mourning on Thursday, the 16th instant, viz.: — [new paragraph] The ladies to wear black dresses, with coloured ribbons, flowers, feathers, and ornaments, or grey or white dresses, with black ribbons, flowers, feathers, and ornaments. The gentlemen to continue the same mourning.

&quot;And on Thursday, the 23d instant, the Court to go out of mourning.&quot;&lt;ref&gt;&lt;cite&gt;&quot;Court Circular: Orders for Court Mourning.&quot; The Morning Post, 2 January 1890 (No. 36,676): page 5 Col. G.&lt;/cite&gt;&lt;/ref&gt;&lt;/blockquote&gt;

===9 January 1890, Thursday===

==== The York Hunt Ball ====
This account is from the ''Irish Society'', which explains which women's costumes are the focus:&lt;blockquote&gt;The fashionable world and his wife are out of town just now, having good times at country houses. They shed the light of their brilliant presence on those annual functions known as county balls, and enjoy themselves also at those popular and picturesque entertainments to which they are bidden by the masters and members of the various hunts.

One of the smartest dances of last week took place at York on Thursday evening. It was in fancy costume, and was in aid of funds for the York County Hospital. Once upon a time the journey from London to the Minster City of the North was a far cry, and one not lightly undertaken. Now it is luxurious and short. In consequence this hall presented the appearance of one in town in mid-season.

There was conspicuous for height and handsomeness the familiar figure and face of Countess de Grey. Lady Helen Duncombe, too, who shares with her Grace of Leinster, and Lady Cynthia Graham, the family beauty of the House of Feversham, was seen in the marvellously becoming (to her) costume of the Empire period. Lady Lilian Wemyss, a lady &quot;divinely tall,” and appropriately fair, was garbed in pink and white of a fashion hailing from the Empire. A &quot;square;” in which the lady dancers were all gowned empirically, was the event of the evening. An event worth remembering it was. The costumes were superb, but their attractions were nowhere in comparison with the charms the [Col. 1c–2a] wearers. These were all tall and each one handsome. Lady de Trafford’s pretty face and fine figure showed to great advantage in her gown of white satin, veiled with gold-bordered ''chiffon'', and with an Empire trained cloak from her shoulders of Rose du Barri velvet lined with white satin, and bordered with gold galon. The colour of the velvet in what is seen in the half-yellow, half-scarlet petals of the soft textured nasturtium bloom. [[Social Victorians/People/Bourke|Mrs Algernon Bourke]] looked a picture in a Gainsborough gown. The white satin skirt was flounced with sable and veiled with ''chiffon'', the setuage of which was left to show without being hemmed up. There was a broad sash of rose-pink silk and each buttonhole was filled round with crimped lisse. One might go on for long enough describing costume after costume, and then leave them half out. Therefore, we shall, like the judge &quot;sum up” and &quot;charge” for a verdict of the utmost brilliancy.&lt;ref&gt;&quot;Our London Letter.&quot; ''Irish Society'' (Dublin) 11 January 1890, Saturday: 17 [of 24], Col. 1b–2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001939/18900111/042/0017. Same print title, p. 29.&lt;/ref&gt;&lt;/blockquote&gt;

===16 January 1890, Thursday===
&lt;blockquote&gt;About two hundred members of the newly formed Dulwich Literary and Scientific Association attended the conversazione given on Jan. 16 at Surrey House Museum, Forest Hill, when Mr. Horniman, F.R.G.S., acted as cicerone round the rooms, richly stored with historical relics, ornithological curiosities, and art treasures.&lt;ref&gt;''Illustrated London News'' (London, England), Saturday, January 25, 1890; pg. 120; Issue 2649, Col. 3.&lt;/ref&gt;&lt;/blockquote&gt;

==February 1890==

=== 12 February 1890, Wednesday ===

==== Lady Constance Leslie's Reception ====
&lt;blockquote&gt;On Wednesday last Lady Constance Leslie had an evening party at her residence in Stratford-place.

The numerous guests included Prince Ernest of Hohenlohe, Princess Victor of Hohenlohe, and the Countesses Gleichen, the Austro-Hungarian Ambassador, Count Mensdorf, Count and Countess Henry Lützow, Mr. and Mrs. Henry White, Baroness de Brienen and Mdlles de Brienen, the Duke of Abercorn, the Duchess of Cleveland, the Marchioness of Blandford and Lady Frances Spencer Churchill, Earl and Countess of Portarlington, Earl Stanhope, the Earl of Northbrook, the Earl and Countess of Arran, the Earl and Countess of Erne and the Ladies Cole, Julia Countess of Jersey and Mr. Brandling, Viscount Clifden, Viscountess Bary, Viscount Torrington, Viscount and Viscountess Castlerosse and Lady Louisa Beauclerk, Viscount and Viscountess de Vesci and Lady Sarah Spencer, Viscountess Galway, and Mr Caryl Ramsden, Lord de L'Isle and Dudley, Lord Alcester, Lord and Lady Wantage, Lord Ashbourne, Lady Henry Grosvenor and Lady G. Ogilvy, Lady Cloncurry, Lord Morris and Mr. M. Morris, Lady Charles Beresford, Lord Rowton, Lady Blanche Hozier, Lady Colville, Lady Rayleigh, Lady Constance Lytton and Mr. Charles Earle, Lady Evelyn Sutton, Lady Ernest Seymour and Ladies Fortescue, Lord and Lady Sandhurst, Lady Mary Lloyd, Lady Tweedmouth, Lady Windsor, Lord and Lady William Seymour, Lady Guy Campbell, Lady Egerton, Lady Fitzgerald, Baron d'Erlanger and Mr. Charles Derenberg, Hon. R. C. Spencer, M.P., and Mrs. Spencer, Hon. Evelyn Ashley, Hon. W. Mansfield, Hon. Lionel Ashley, Hon. A. Hood, Hon. William Lowther and Miss Lowther, Hon. Sydney Greville, Hon. Fitzroy and Mrs. Stewart, Hon. Frederick Leveson Gower, Hon. Kenneth Howard, Hon. Francis Villiers, Hon. Francis Bertie, Hon. Arthur Walsh, Colonel the Hon. Charles Edgcumbe, General Hon. John Bourke, General and Hon. Mrs. Ellis and Mrs. R. Sneyd and Miss Ellis, [[Social Victorians/People/Bourke|Hon. Algernon and Mrs. Bourke]], Hon. Alan and Hon. Evan Charteris, Hon. Alexander Yorke, Hon. Derek Keppel, General Sir Dighton Probyn, Hon. Percy Wyndham, Hon. Everard Baring and Hon. Susan Baring, Hon. Mrs. Brett, Hon. Claud Hay, the Right Hon. Henry Matthews, Sir George Arthur, Sir George Maude, Sir Philip Currie, C.B., Sir Redvers and Lady Audrey Buller, Sir Charles Grant, Sir Mackenzie Wallace, Sir Herbert Maxwell, M.P., Sir Oscar Clayton, Sir Robert Gresley, Sir Algernon West and Mr. Horace West, Sir George and Lady Russell and Miss Brackenbury, Sir Henry and Lady Longley, the Sub-Dean of the Chapels Royal, General Crealock, General Charles Fraser, Colonel Saunderson, M.P., and Hon. Mrs. Saunderson, Colonel and Mrs. Stewart and Miss Streatfeild [siv], Colonel and Miss Balfour, Colonel and Mrs. Stanley Clarke and Miss Clarke, Colonel R. Baring, Captain and Mrs. Jekyll, Captain and Mrs. J. Bagot, Captain Lambert Ward, Captain A. Bagot, Mr. Charles Hall, Q.C, M.P., Mr[.] Hussey Walsh, M.P., Mr and Mrs. W. Hartpole Lecky, Mr. and Mrs. Richard Combe, Mr Henry Foley, Mrs. Arbuthnot and Miss Guthrie, Mr. and Mrs. Heseltine and Miss Dorothy Heseltine and Lord Cantelupe, the Miss Stopford Brooke, Mr. and Mrs. Thackeray Ritchie, Mr Edmund Byng, Mr. and Mrs. Wilton Phipps, Professor Sidney Colvin, Mr. and Miss Tennant, Mr. Godfrey Webb, Mr. and Mrs. Turton and Mr. Sidney Ponsonby, Mrs. Adare, Mrs Cecil Paget and Mr. Hugo Wemyss, Mrs. L. Drummond, Mr. and Mrs E. Hope, Mrs. L. Seymour and Miss Seymour, Mr. Guy Repton, Mr. and Mrs. Julian Sturgis and Miss Beresford, Mr. Poynter, R.A., Mrs. Daniel Cooper, Mr. Hamilton Aïdé, Mr. Alwyne Maude, Mrs. C. Bentinck, Mrs. Bingham Mildmay, Mr. Philip Habord, Mr. and Mrs. George Bulteel, Mrs. Beerbohm Tree and Miss Julia Neilson, Mr. Hallé [Halle?], Mr. Rudolph Lehmann and Miss Lehmann, [[Social Victorians/People/Fanny Ronalds|Mr. R. Ronalds]], Mr. Ellice, Mr. Arthur, Madame Blumenthal, Miss Julia Leslie, Mr. and Mrs. Jeune, Mr and Mrs. Charles Stuart-Wortley and Misses Millais, Mrs. Arkwright, Mr Joachim, Mr. Gillett, Mr. Pulteney (Scots Guards), Colone| Cuthbert Larking, Mr. Harry Higgins, M. Tividar Nachez, Mr. G. Ross, Herr Johannes Woolff, Mrs. Charles Bagot and Miss Bagot, Mrs. Bischoffsheim, Mr. Henry Petre, Miss Balch, Mr. and Lady Maud Ramsden, Mr. Adolphus Liddell, Mr Knowles, Mr. Grenfell, Mr. Edward Hamilton, Mrs. Henry Gordon and Miss Gordon, Mr. Henry James, Mr. St. Leger, Mrs. Dacre Hamilton and the Misses Nugent, Mr. Harbord, Mr Somerset, Mr. Ruggles-Brise, Mr. and Miss Hughes of Kinmel, Mr. and Mrs Douglas Freshfield, Mrs. Homer, Mr. W. H. Mallock, Mr. and Mrs. Robert Benson, Mr. H. Seymour, Mr. Ernest Law, Mr. Hugh Grimston, Mr. Lionel Cust, Mr. Chappell, Mr. and Mrs. Du Maurier, Mr. Boughton, R.A., and Mrs. Boughton, Mr. R. Roche, Mr. Montagu Wilson, Mr. Herbert Hope, &amp;c.&lt;ref&gt;&quot;Lady Constance Leslie's Reception.&quot; ''Morning Post'' 15 February 1890, Saturday: 2 [of 8], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18900215/008/0002. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

=== 24 February 1890, Monday ===
Lilly Langtry starred in Shakespeare's ''As You Like It'' at the St. James's Theatre. The Daily Telegraph had a long review and mentioned more names:&lt;blockquote&gt;
The motto of Petronius, which is said to have adorned the Globe Theatre in Shakespeare's time, &quot;Totus mundus agit histrionem,&quot; and which is reproduced in Jaques' famous speech, may be said to have received a novel illustration in the brilliant audience which completely filled the St. James's Theatre last evening. A very distinguished section of the world &quot;played the actor&quot; in the stalls, boxes, and dress-circle, and evinced the keenest dramatic interest in the long-deferred production of &quot;As You Like It.&quot; The Prince and Princess of Wales, with the Duchess of Fife, surveyed the scene from the Royal box, while amongst the many who secured seats for the first were the Austrian Ambassador, the [[Social Victorians/People/Louisa Montagu Cavendish|Duchess of Manchester]], Countess de Grey, [[Social Victorians/People/Mandeville|Viscountess Mandeville]], Lady Colin Campbell, Lord Wolverton, Lord and Lady Coleridge, Sir Charles Russell, Sir Edward and Lady Guinness, Baroness de Stern, and Mr. Alfred Rothschild. Naturally enough there was much curiosity in seeing once more on the London stage an actress who has since her last appearance devoted so much serious study to her profession, and gained so much success both before American and provincial audiences; while the sympathy evoked by her recent severe illness, delaying for four weeks the production of the comedy, added an almost pathetic note to the general excitement and enthusiasm. In the second scene of the first act, when the tenderly attached cousins make their earliest appearance on the stage, Celia's first words, &quot;| pray thee, Rosalind, sweet, my coz, be merry,&quot; answered by Rosalind’s &quot;Dear Celia, I show more mirth than I am mistress of,&quot; were almost drowned in the applause which accompanied the  recognition of Mrs. Langtry. From time to time, whenever opportunity served, enthusiasm broke out anew, culminating in the triumph of plaudits which formed the fit ending to the gracefully-delivered epilogue with which Rosalind takes her farewell of her audience. There can be no doubt that, with all due allowance for the inevitable nervousness which accompanied a first production before a critical though sympathetic house, the revival of the immortal comedy was generally pronoanced to be a success.

The fancifally-named &quot;As You Like It&quot; — where even in nomenclature the author confesses his indebtedness to the romance of Thomas Lodge — with greater dullness than is usually the case with Shakespeare's plays. Indeed interest is hardly aroused till the scene before the Duke's Palace, where Rosalind and Celia witness the wrestling — which after a few more performances will probably go less stagily than it did last night — between Charles and Orlando. It is only when we are transported to the Forest of Arden that Shakespeare's romantic fancy allows itself full course, and it was only when she was accoutred in the doublet and hose that Mrs. Langtry exercised her full charm upon the audience. The difficulty for the actress in the character of Rosalind is the contrast between the early abandon of her frankly-expressed love for the son of Rowland de Bois and the subsequent archness and reserve with which she plays with her lover in the forest. Orlando goes through precisely an opposite change. From the careless desperateness of a man who is out of favour with fortune in the opening scene, he changes to the sentimental devotion of a &quot;love-shaked fancy-monger&quot; in the sylvan glades. If that interchange of parts be missed much is lost in the sprightly  contrasts of the drama. Unfortunately, no sooner did Orlando enter on the wrestling-ground last night, than he started and caught at his heart in obvious suggestion of love at first sight. Much is lost of the utter wonderment at Rosalind’s unexpected graciousness in giving him her chain, which keeps him tongue-tied later, if he betrays so early the fatal ravages of Cupid — a betrayal which is hardly likely in a man whom neglect and misery have driven to the last stage of reckless hardihood. Rosalind must love her champion before her winning thanks for his prowess have made the starred younger brother first marvel at and then adore the frank and generous advances of his benefactress. In the fine words, &quot;My father was no traitor,&quot; Mrs. Langtry rose to the full height of the character she was depicting. Throughout the greater part of the first act there was grace, loveableness, charm, but also a kind of flatness, or, at all events, an even and somewhat uninteresting level of characterisation which did not convey the promise of all that this loveliest creation in Shakespeare's gallery could do, when the Court life was exchanged for the freer and less conventional existence in the woods.

All the more praise, therefore, is Mrs. Langtry’s due, that when she finds herself in the Forest of Arden, she brings before us a truer Rosalind. The beautiful first scene between the disguised Ganymede and her amorous swain showed Mrs. Langtry at her best. The quick and nimble wit, the archness and pretty coquetry of a girl who is sick at heart with love and feeds her passion in a playful and adorable tyrannising over the unconscious lover, were depicted with a reality which won instant recognition from the spectators. For the rest, however, Mrs. Langtry’s Rosalind was an unequal performance, now rising with unexpected force into the regions of pure comedy, now sinking to an ordinary level of  uncomfortably-disguised womanishness. There were bright patches of power in the midst of a somewhat dull and colourless expanse. Much of this was, no doubt, due to the excitement and fatigue of a first night, to which also may be attributed possibly the sameness of some of her gestures and a restlessness which was something more than Rosalind's anxiety to win in her own incomparable way the happiness of which she was in search. A few nights hence firmness of carriage and self-control of manner will fill in the details of a character which was most graphically and sympathetically sketched in outline at the St. James’s last night. Mr Laurence Cautley as Orlando made most favourable impression on his audience. Through all the earlier scenes — with the exception of that wholly unnecessary lapse into amorousness on the lawn of Duke Frederick, which has been already noted — he sustained the character of a picturesque and youthful gallant with considerable success, though, possibly, a stronger dash of manly independence might not have come amiss to the Shakespearean hero. Touchstone is a more difficult part to play. Indeed, in some respects, he is the most difficult of all Shakespeare's clowns. He is on the borderland between the earlier, more conventional style of Costard, Launce, and Launcelot, and the far more elaborate and important clowns in &quot;Twelfth Night&quot; and &quot;King Lear.&quot; He is not so clever as Feste, not so human and real as that inimitable and tender-hearted Edgar who tries to solace the wild ravings of his discrowned king. He is halfway between such farcical beings as Kempe and Tarlton probably depicted, and that witty, self-conscious, irresponsible Jester, which Shakespeare ultimately made an entirely new creation on Elizabethan boards. It is no discredit to Mr. Sugden that he failed to realise so ingenious a conception. He presented a Touchstone who was full of amusing quips, and he went through all the catalogue of points in the Book of Honour in the fifth act with admirable skill; the Touchstone of &quot;As You Like It&quot; we are probably not likely to see often on the modern stage. Mr. Bourchier’s Jaques was a far higher piece of portraiture, grave and bitter and cynical as that early disciple of Schopenhauer should be, with touches of humour which only serve to show the depths of a naturally perverse and misanthropical nature. The celebrated &quot;Seven Ages&quot; speech  was capitally delivered, with a conscientious care and easy mastery which are rare enough in an actor who has so lately left the ranks of the amateurs. For the rest, the Adam of Mr Everill, and the Andrey of Miss Marion Lea seemed to give most pleasure to the audience, though she was sometimes — espectally in the pronunciation of the word &quot;poetry&quot; — inclined to represent the boorishness of the wench with an accent  which reproduced simulated inebriation rather than native clumsiness. Miss Armbruster as Hymen also deserves a word of praise. The piece was produced under the direction of the Hon. Lewis Wingfield, and the scenery, which in the Forest Glade of Acts II., III., and IV., formed a beautiful stage picture, was designed by Messrs. Perkins and Bruce Smith.

After all, was any one ever wholly satisfied with the representaton of one of Shakespeare's comedies? No thing is further from the truth as a general statement than the pedant’s theory that Shakespeare is for the study, and not for the boards. If ever, however, the paradox be true that a great dramatic artist suffers when his plays gain a dramatic representation, it is when &quot;As You Like It,&quot; &quot;Twelfth Night&quot; and &quot;Midsummer Night's Dream&quot; are brought face to face with a modern audience and amid nineteenth century surroundings. It ts not with impunity that the light that never was on sea and land is parodied by the glare of the footlights. For, honest stage-craftsman as Shakespeare was, in the full spring-tide of his poetic genius there was a divine and masterful intolerance of the real and the commonplace, a reckless flight into an ideal world, peopled by beings coined in the mint of his dainty imagination — aerial and disembodied creations whose actions and characters refuse to submit themselves to the narrow rules of the every-day world. In such a sphere banished lovers shall be predestined to meet and cement their happy unions, and lions and snakes shall be the habitual denizens of a forest where shepherds and shepherdesses prattle their erotic strains, and even a crafty Oliver shall repent of his past sins and fall in love with gentle Celia, owing to the poetic exigencies of Cloud Cuckoo Land. How can one  see all these things with the cynical eye of the modern ''Fin de Siècle'' and not feel an inevitable shock of dissatisfaction and surprise? How is it possible to avoid the jarring sense of discord when the dream picture is realised in the setting of prosaic reality? For Shakespeare's comedy is a romantic work of the mind, a refuge for all those delightful improbabilities which an indolent or whimsical fancy strings together to construct a series of complications and incidents which interest us, while they elude the sober tests of reason and judgment. But we must not carry this vein of thought too far. It is true that we have in such plays comedies of incident rather than of character. Yet Shakespeare is too and heart-whole to linger only at the Ivory gate. He throws even into these merry plots the force of that instinctive knowledge of human nature which produces real personages, tricked out in witty and imaginative guise. Shakespeare was able to pour everything into his comedies which he did into his tragedies, though in the one there is only suggestion, while in the other there is the elaboration of that is deep and tragic as well as humorous in life. Rosalid, Orlando, Touchstone, and Jaques are none the less real because they are ideal; and it is on these grounds that we can praise the conscientious and capable artists who presented these characters in flesh and blood on the St. James's stage. Nor does Shakespeare, as some have thought, intend in this play to preach [Col. 1c–2a]  any polemic against the life of the town, or compose any passionate encomium for the simple graces of the country. He is too great to be didactic on such narrow issues. Wherever men and women live, there they can be happy; or, as Touchstone says to Corin, when he expresses ignorance of the Court, one-sided enthusiasts for either streets or hedge-rows are truly damned, &quot;like an ill-roasted egg, all on one side.&quot; Equanimity, such that of the Duke and old Adam, carries with it, wherever it be, the gracious gentleness of an eternal Eden.&lt;ref&gt;&quot;St. James's Theatre.&quot; ''Daily Telegraph &amp; Courier'' (London) 25 February 1890, Tuesday: 5 [of 12], Col. 6a–7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001112%2F18900225&amp;page=5&amp;article=048&amp;stringtohighlight=mandeville+viscount. Print title: ''The Daily Telegraph'', p. 5.

&lt;/ref&gt;&lt;/blockquote&gt;
The ''St. James's Gazette'' reported:&lt;blockquote&gt;
We came intending to like it very much, and we succeeded in our intention. Indeed, we spent a really pleasant evening at the St. James's Theatre, Many of us knew one another to nod to, and some of us had bowing acquaintance with the author of the play; so it was all very sociable and comfortable. There were just enough shop-window celebrities to give an air of distinction to the rest of the audience, and everybody had a right to hope that his neighbours were wondering who he was. The critics were quite at their ease, having nothing to criticise except the acting; not being expected to suggest any slight alterations in the play (such as cutting out Acts I., III., and V., and rewriting Acts II. and IV.), but just to accept it as it stood, without even tracing it back to the French vaudeville from which it was, no doubt, originally adapted.

The performance had many individual merits, but it also had two general faults. The first and least striking fault was that the interludes were  slurred over instead of being played up to. Now, the plot of &quot;As You Like It&quot; is so loose that a lengthy interlude (provided it be pretty) does not check the flow of interest; indeed, it gives a welcome rest and allows you to pick up your thoughts again. The other fault is one which may be, and is likely to be, remedied the play goes on. But at present it is neither smart nor spontaneous: the parts do not hang well together, and there is none of the enthusiasm which helps to pass off the interior performances of less skilful actors. The deficiency which we have noted was probably due to the serious illness from which Mrs. Langtry had been suffering and from which it was evident last night that she had not made a complete recovery. She worked very hard as Rosalind, and worked very well, and several times she made a really good hit; she was, perhaps, at her best in her indignant appeal to the usurper Duke against his unexpected and unjust decree of banishment. She was charming, again, in her embarrassment (as Miss Litton was charming before her) when she had her first meeting with her unconscious lover and she suggested very cleverly the absence of her skirts. She did her love-making archly and merrily; but though the pretended pretence gave her a right to go beyond the limits of maiden coyness, she seemed occasionally to assume the masculine Initiative when the feminine Suggestive would have been prettier. it was a pleasant though uneven performance, with plenty of grace in it and plenty of brains. The Touchstone of Mr. Sugden was in every way admirable — crisp, humorous, and distinctive. That his clowning was occasionally tedious was no fault of his. The palate of a modern audience does not relish these long-drawn pedantries of buffoonery. Our sense of humour is not more refined — it is different, and that's the end of it. But in the scenes with Audrey (and Miss Marion Lea made a capital Audrey — open-mouthed and innocently wicked or wickedly innocent) Mr. Sugden had a better opportunity and he made the most of it. There the humour was not conventional, and the audience enjoyed a laugh which was not scholarly. A word of praise must given to Mr. Brodie for his conscientious and effective rendering of the difficult and ungrateful part of the moonstruck lover of the wayward Phoebe. The first appearance of Mr. Bourchier in London attracted much interest. As an amateur at Oxford and elsewhere he was believed Iikely to to great things upon the stage, and his performance of Jaques was by no means a disappointment. The fault of it was that he did not suggest either the melancholy or the sententiousness which we associate with the character. The melancholy was but skin-deep, and the sententiousness simply was not there. But every actor has a right to read a part in his own way if it is a good way. And there is much to said for Mr. Bourchier's interpretation of Jaques. The temptation is to be stagy; Mr. Bourchier's tendency is to be natural. And he carried it out with great success in speaking the lines of the Seven Ages of Man. He caught up the Duke's phrase just as if it had dropped in the course of an ordinary conversation; and he played with it for a time until it seemed of itself to suggest to his mind the famous soliloquy. Certainly Mr. Bourchier’s method was effective, as it drew one of the heartiest rounds of applause in the whole evening.

Among the company were noticed the following well known persons:— His  Royal Highness the Prince of Wales, the Duke and Duchess of Fife, [[Social Victorians/People/Mandeville|Lady Mandeville]], Lord De Grey, Mr. Alfred De Rothschild, Lord Lurgan, Sir Charles Russell, Sir Edward Guinness, Lady Colin Campbell, Lady Curzon, Lady Londonderry, Lady Hothfield, Hon. Alan Charteris, Mr. Oscar Wilde, Mr. Akers Douglas, M.P., Mr. Justin McCarthy, M.P., Sir Allen Young, Lord and Lady Coleridge, the Austrian Ambassador, the Spanish Ambassador, Lady Hozier, Mr. George Lewis, Mr. Whistler, Lady Greville [&lt;nowiki/&gt;[[Social Victorians/People/Lady Violet Greville|Lady Violet Greville]]?].&lt;ref&gt;&quot;As You Like It.&quot;  ''St James's Gazette'' 25 February 1890, Tuesday: 5 [of 16], Col. 1b–c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001485%2F18900225&amp;page=5&amp;article=027&amp;stringtohighlight=mandeville+viscount. Same print title and p.

&lt;/ref&gt;&lt;/blockquote&gt;
This report is from ''Blalud, The Bath Society Paper'':&lt;blockquote&gt;Happily, there was no disappointment in store for the friends and admirers of Mrs. Langtry, who gathered on Monday night at the St. James’s Theatre in great force, to welcome this popular lady back to London and receive her with an extra warmth of cordiality in token of satisfaction at her recovery from her recent severe illness. Eight years have elapsed since she last played Rosalind in London. Since then she has travelled much, both at home and abroad, and followed the study and practice of her art with unfailing spirit and determination. She returns to the character which all leading actresses aspire to play in Shakespeare’s glorious dream of the Court of Duke Frederick and the forest of Arden a far riper artist, and, says the ''Daily News'', she presented us on Monday with an impersonation which compared to her former efforts is as the finished portrait to the crude sketch. Her performance may lack the great high tide of girlish impulsiveness, but first nights before an exceptionally critical audience and some remains of the languor of her recent indisposition doubtless contributed to rob her acting of something of its force and impulse. But her ''Rosalind'' remains a most winning and beautiful performance. A handsomer ''Rosalind'', or one that has worn the doublet and hose with more grace and picturesqueness (Mrs, Langtry, we may here note, scorns the modern heresy of boots, and appears in the more orthodox hose cross-gartered), has certainly not been seen in our time. The performance is full of good points; as when at the words, &quot;here on the skirts of this forest like the fringe of a petticoat,&quot; she remembers with a momentary touch of maidenly shyness that petticoats no longer form part of her attire. Again, when in bantering her lover, who exhibits so strange an inability to recognize the voice and features of the woman whom he passionately loves, she pauses at &quot;a beard neglected,&quot; and pointing at ''Orlando’s'' smooth chin bursts into uncontrollable laughter; again, when in the mock marriage scene, with ''Celia'' for the priest, her mind for the moment seems to wander away into such a dream as this mockery might suggest to one so deeply in love. The distinguishing feature of the impersonation, indeed, is the subtle suggestion of serious passion that underlies the frolicsome and bantering moods, and exhibits itself again and again in many subtle forms. The play is beautifully put on the stage, and if some of the performers fall a long way short of ideal excellence there are several impersonations that stand forth in strong relief and are of far more than common excellence. The ''Phœbe'' and ''Silvius'' of Miss Beatrice Lamb and Mr. Matthew Brodie deserve special note: but the most brilliant success of all in the case of the minor characters was undoubtedly the ''Audrey'' of Miss Marion Lee, whose hoydenish, but not ungraceful antics, whose happy, contented ignorance, whose mingled wonderment and admiration at ''Touchstone's'' philosophical utterances were admirable. Everything that taste can suggest has been done to embellish the play; the musical features are strengthened by an efficient chorus, and the costumes designed by the Hon. Lewis Wingfield are rich and handsome. Perhaps it might be objected that Mrs. Langtry’s beautiful green velvet doublet, with its slashes, tags, and laces, her cinnamon jerkin, her black cap and jewelled buckle, and her rich and massive cloak were hardly suited to her daring enterprise on the highways and in the forests of the Duke’s dominions. The restoration of Hymen, gracefully represented by Miss Violet Armbruster, and the final morris dance in honour of the nuptials, gave the crowning fanciful touch to the performance, and prepared the spectators for the playful epilogue, which was spoken by Mrs. Langtry, in her simple nuptial white robe and leopard skin, with rare elocutionary grace and effect,. [sic]

The audience which greeted Mrs. Langtry was at once distinguished and interesting. The Royal box was occupied by the Prince and Princess of Wales, the Duchess of Fife, the Princesses Victoria and Maud of Wales, and the Duke of Fife. Among the representatives of &quot;Society&quot; were Lady Londonderry, [[Social Victorians/People/Mandeville|Lady Mandeville]], Lord de Grey, Lord and Lady Coleridge, Lady Curzon, Lady Hothfield, Lord Lurgan, Lady Greville [&lt;nowiki/&gt;[[Social Victorians/People/Lady Violet Greville|Lady Violet Greville]]?], Lady Hozier, Mr. Alfred de Rothschild, Sir Charles Russell, Sir Edward Guinness, Mr. Coningsby Disraeli, Mr. Akers Douglas, M.P., Mr. Justin M‘Carthy, M.P., Sir Allen Young, Lady Colin Campbell, Lady Monckton, Mrs. Labouchere, and the Austrian and Spanish Ambassadors. Pictorial art was represented by Mr. Whistler; music by Mdme. Antoinette Sterling; dramatic writing by Mr. H. A. Jones; and theatrical interests by Mrs. Bancroft, Miss Genevieve Ward, Mr. and Mrs. John Lart, Mrs. John Hare, Mr. M. L. Mayer, Mr. Augustus Harris, &amp;c.&lt;ref&gt;&quot;Mrs. Langtry.&quot; ''Bladud'' 26 February 1890, Wednesday: 9 [of 16], Col. 2b–c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0005771%2F18900226&amp;page=9&amp;article=055&amp;stringtohighlight=mandeville+viscount. Print title: ''Blalud, The Bath Society Paper'', p. 9.&lt;/ref&gt;&lt;/blockquote&gt;

=== 25 February 1890, Tuesday ===
On 5 March, the ''World'' reports on a party hosted by Mrs. Adair that must have been held the week before:&lt;blockquote&gt;Many smart people were present at Mrs. Adair's party in Curzon Street on Tuesday night. The rooms, lighted by electricity, looked their prettiest with floral decorations consisting entirely of tulips, the hostess appearing in a gown of terra-cotta velvet trimmed with dark fur. The Austrian Ambassador and Madame Waddington were among those who listened to Miss Damian’s rendering of a new song by Tosti, and to the glees sung by Mr. Avon Saxon's American quartet; and among others present were Lady Charles Beresford, [[Social Victorians/People/Mandeville|Lady Mandeville]], the Duchess of Marlborough, Lady Fanny Marjoribanks, who brought her sister, Lady Sarah Churchill, Sir Arthur Sullivan (just back from his annual sojourn at Monte Carlo), Lord and Lady Wharncliffe, Lady Howe and Lady Edith Curzon, Lord and Lady William Nevill, Mrs. Cavendish-Bentinck, General Charles Fraser, Lady Conyers, Madame de Brienen, and Sir Philip Currie.&lt;ref&gt;&quot;What the World Says.&quot; ''The World'' 5 March 1890, Wednesday: 19 [of 44], Col. 2a [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0006339%2F18900305&amp;page=19&amp;article=061&amp;stringtohighlight=mandeville+viscount. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;The ''Daily Telegraph'' covered the party with a few additional names:&lt;blockquote&gt;A casual passer-by in Curzon-street last night might almost have imagined from the long string of carriages assembled there that, in spite of the cold east wind blowing, the London season had already begun. Mrs. Adair had together to hear some beautiful music, including a celebrated quartette of American singers, a large and fashionable crowd, composed of the ''élite'' of London society, comprising among many others, the Austrian Ambassador, the French Ambassadress, the Marquis and Marchioness of Tweeddale, Lady Charles Beresford, Lady Fanny Marjoribanks and Lady Sarah Spencer-Churchill, Earl and Countess of Wharncliffe, Countess Howe and Lady Edith Curzon, Lord and Lady William Nevill, Lord George Nevill, Viscount and Viscountess Curzon, Countess of Sefton and Lady Rose Molyneux, Viscountess Mandeville, Julia Countess of Jersey and Mr Brandling, Viscount and Viscountess Bury and the Hon. Mary Keppel, the Countess of Crawford, the Earl of Clonmell, the Countess of Antrim and Lady Louisa Beauclerk, Viscountess Melgund, Lady Conyers, Hon. Lady Cotterell and Miss Cotterell, Lord Alington, Lord Alcester, Lord Greenock, Viscount de Vesci, Lady Hilda Brodrick, Hon. W. Lowther, M.P., and Mrs. Lowther, Hon. Mrs. Bampfylde, Hon. Hallyburton Campbell, Mrs. and Miss Campbell, Hon. Kenneth Howard, Hon. Derek Keppel, Hon. FitzRoy and Mrs. Stewart, Lady FitzGerald, Mrs. Bischoffsheim, Madame de Brienen, Lieutenant-General Sir Seymour Blane, General C. Fraser, M.P., Mr. Chamberlain, M.P., Mr. Howard Vincent, M.P., and Mrs Vincent, Mr. Charles Hall, M.P., Mrs. Cavendish-Bentinck, Sir C. Rivers Wilson, Sir Arthur Sullivan, Sir Philp Currie.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph &amp; Courier'' (London) 26 February 1890, Wednesday: 5 [of 8], Col. 4a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001112%2F18900226&amp;page=5&amp;article=094&amp;stringtohighlight=mandeville+viscount. Print title: ''The Daily Telegraph'', p. 5.

&lt;/ref&gt;&lt;/blockquote&gt;The ''Sporting Gazette'' also had a report, on 1 March:&lt;blockquote&gt;Mrs. Adair's party in Curzon-street on Tuesday night was, as usual, exceedingly smart and dressy. The &quot;smarties&quot; turned out strong for this Anglo-American function, and wore their best frocks and jewels. Lady Tweeddale, Lady Howe, with Lady Edith Curzon, Lady Fanny Majoribanks chaperoning her younger sister, Lady Sarah Churchill, Lady Curzon, Lady Antrim with Lady Louisa Beauclerk, Lady William Nevill with some lovely diamonds, [[Social Victorians/People/Mandeville|Lady Mandeville]], Lord Alington, Sir Arthur Sullivan, Mrs Cavendish Bentinck, and others. The singing of an American quartette was ''the'' feature of the evening.&lt;ref&gt;&quot;The Man About Town.&quot; &quot;The County Gentleman.&quot; ''Sporting Gazette'' 1 March 1890, Saturday: 6 [of 38], Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0002525%2F18900301&amp;page=6&amp;article=053&amp;stringtohighlight=mandeville+viscount. Same print title, p. 274.&lt;/ref&gt;&lt;/blockquote&gt;

==March 1890==

=== 10 March 1890, Monday ===
The Prince and Princess of Wales hosted a ball in celebration of their wedding anniversary.

This report from the ''Bedfordshire Mercury'' is very brief:&lt;blockquote&gt;
The Prince and Princess of Wales, in celebration of the anniversary of their wedding on March 10, 1863, gave a dance at Marlborough House on Monday night. The Danish Minister and Madame de Falbe were among the company invited, also the Earl and Countess Brownlow, [[Social Victorians/People/Mandeville|Viscountess Mandeville]], Lord Alwyne Compton, Baron F. de Rothschild, &amp;c.&lt;ref&gt;&quot;Notes of the Aristocracy.&quot; ''Bedfordshire Mercury'' 15 March 1890, Saturday: 7 [of 8], Col. 4b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001290%2F18900315&amp;page=7&amp;article=073&amp;stringtohighlight=mandeville+viscount. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;
The report from the ''Morning Post'' suggests that this was a smaller party than usual for the Prince and Princess of Wales:&lt;blockquote&gt;In celebration of the anniversary of the Prince and Princess of Wales's wedding day, their Royal Highnesses gave an evening party (dancing) at Marlborough House last night.

His Royal Highness the Duke of Edinburgh, her Royal Highness Princess Beatrice (Princess Henry of Battenberg) and his Royal Highness Prince Henry of Battenberg, her Royal Highness the Princess Louise of Wales (Duchess of Fife) and the Duke of Fife, his Royal Highness Prince George of Wales, her Royal Highness the Princess Victoria of Wales, her Royal Highness the Princess Maud of Wales, her Royal Highness the Princess Mary Adelaide (Duchess of Teck), and his Highness the Duke of Teck and her Serene Highness the Princess Victoria of Teck and his Serene Highness Prince Francis of Teck, and their Serene Highnesses the Prince and Princess Victor of  Hohenlohe-Langenburg and the Countess Victoria Gleichen were present.

The following had the honour to receive invitations, but some amongst them were unavoidably prevented from attending: —

The French Ambassador (M. Waddington) and Madame Waddington, the German Ambassador (Count Hatzfeldt) and the Countess Marie Hatzfeldt, the Turkish Ambassador (Rustem Pasha), the Austro-Hungarian Ambassador (Count Deym) and the Countess Deym, the Italian Ambassador  (Count Tornielli), the Countess Tornielli, and Mademoiselle Virginia dei Conti Lazzari, the Danish Minister (M. de Falbe) and Madame de Falbe, the Russian Chargé d'Affaires (M. Bontineff), his Serene Highness Prince Louis Esterhazy, M. A. Kroupensky, M. A. de Stoeckl, Count Leyden, Count Albert Mensdorff, Count Reventlow, Mr. and Mrs. Henry White, M. de Soveral, the Marques and Marquesa de Santurce, Mr. A. de Murrieta, Mr. C. de Murrieta.

The Duke and Duchess of Leeds and Lady Alice Osborne, the Duke and Duchess of Buccleuch, the Duke and Duchess of Portland, the Duke and Duchess of Westminster, the Marchioness of Blandford and Lady Frances Spencer Churchill, the Marquis and Marchioness of Granby, the Marquis and Marchioness of Londonderry, the Marquis and Marchioness of Ormonde, the Marquis and Marchioness of Salisbury and Lady Gwendolen Cecil, the Marquis and Marchioness of Stafford, Count Gleichen, the Earl and Countess Brownlow, the Earl and Countess Cadogan and Lady Emily  Cadogan, the Earl and Countess of Clarendon, the Earl of Chesterfield, the Earl of Clonmell, the Earl of Dudley, the Earl and Countess of Dunraven and Lady Florence Wyndham Quin, the Earl and Countess Granville and Lady Victoria Leveson Gower, the Earl and Countess of Hardwicke, the Earl and Countess Howe and Lady Evelyn Curzon, the Earl and Countess of  Kilmorey, the Earl and Countess of Lathom and Lady Alice Wilbraham, the Earl and Countess of Lucan and Lady Rosalind Bingham, the Earl of Mount Edgcumbe and Lady Albertha Edgcumbe, the Earl and Countess of Romney and Lady Florence Marsham, the Earl and Countess of Rosebery, the Earl of Shaftesbury, the Earl of Stradbroke, the Earl and Countess of Sefton and Lady Gertrude Molyneux, the Earl and Countess Spencer, Viscount Drumlanrig, Lord and Lady Randolph Spencer Churchill, Lord Frederick Hamilton, Lord Ernest Hamilton, Lord and Lady Algernon Gordon Lennox, [[Social Victorians/People/Mandeville|Viscountess Mandeville]], Lord Charles Montagu, Viscount Chelsea, Viscount and Viscountess Coke and the Hon. Violet White, Viscount Curzon, Lady Georgina Curzon and Lady Sarah Spencer Churchill, Viscount Fincastle, Viscount Royston, Viscount Valletort, Lord and Lady Brooke, Lord Burghersh, Lord Capell, Lord and Lady Norreys and the Hon. Coralie Glyn, Lady Charles Beresford, Lord Marcus Beresford, Lord Alwyne Compton, Lord and Lady William Nevill, Lord Richard Nevill, Lord Henry Paulet, Lord Henry Vane Tempest, Lord Herbert Vane Tempest, Admiral Lord Alcester, Lady Ampthill and the Hon. Constance Russell, Lord Alington and the Hon. Winifred and Hon. Mildred Sturt, Lord and Lady Colville of Culross  and the Hon. Blanche Colville, Lord and Lady De  Ramsey, Lady Hastings, Lord and Lady Hindlip, Lord Lurgan, Lord and Lady Revelstoke and the Hon. Susan Baring, Lord and Lady Rothschild,  Lord Rowton, Lord Suffield and the Hon. Judith and Hon. Eleanor Harbord, Lord and Lady Wimborne and the Hon. Frances Guest, Lord Wolverton, Baron Ferdinand Rothschild, Captain the Hon. Maurice Bourke, R.N., Colonel the Hon. Henry Byng and the Misses Byng, the Hon. Alan Charteris, Lieutenant-Colonel the Hon. C. Edgcumbe, the Hon. Sir Spencer and Lady Ponsonby Fane, the Hon. Sidney Greville, Colonel the Hon. Oliver Montagu, the Hon. C. R. and Mrs. Spencer, the Hon. S. M'Donnell, the Hon. Alexander Yorke, the Hon. H. and Lady Feodora Sturt, the Hon. Arthur Walsh, the Hon. R. Winn, the Right Hon. W. E. and Mrs. Gladstone and Miss Gladstone, the Right Hon. A. J. Balfour, the Right Hon. H. Chaplin, the Right. Hon. Sir Henry James, the Right Hon. Sir C. L. Wyke, the Hon. S. C. Colville, the Hon. Assheton Harbord, the Hon. Julia Stonor, the Hon. H. Stonor, the Hon. E. Stonor, Captain the Hon. Henry White, Sir Edward and Lady Guinness, Sir Charles Hartopp, Sir Frederick Johnstone, Sir John and Lady Lister Kaye, Sir James and Lady  Mackenzie, Colonel Sir Nigel and Lady Emily Kingscote, Admiral Sir R. and the Hon. Lady Macdonald and Miss Macdonald, General Sir Dighton and Lady Probyn, Sir Francis and the Hon. Lady Knollys, Major-General Sir Christopher Teesdale, Sir Oscar Clayton, Sir Allen Young, Lieutenant-General Bateson, Lieutenant-General Charles Fraser, Major-General and the Hon. Mrs. Arthur Ellis and Miss Ellis, Colonel J. P. Brabazon, Colonel and Mrs. Stanley Clarke and the Misses Clarke, Captain H. F. Stephenson, R.N., Lieutenant-Colonel F. H. Poore, Lieutenant-Colonel R. Vivian, Major C. Swaine, Captain Douglas Dawson, Captain C. H. A. Hervey, the officers of the Queen's Guard, St. James's Palace, Mr. G. Byng, Mr. Henry Calcraft, Mr. Victor Cavendish, Mr. Henry Ellis, Mr. Horace Farquhar, Mr. and Mrs. George Forbes and Miss Forbes, Mr. Montagu Guest, Mr. Charles Hall, Mr. E. W. Hamilton, Mr. and Lady Hilda Higgins, Mr. Holzmann, Miss Knollys, Mr. and Mrs. F. R. Knollys, Mr. Ronald Moncrieffe, Mr. Alfred Montgomery, Mr. Arnold Morley, Mr. Henry Petre, Mr. Alfred de Rothschild, Mr. and Mrs. Leopold de Rothschild, Mr. Reuben Sassoon and Miss Sassoon, Mr. and Mrs. Arthur Sassoon, Mr. Edgar Sebright, Mr. and Mrs. Ralph Sneyd, Mr. Christopher Sykes, and Mr. O. G. St. George Williams.

Messrs. Coote and Tinney's band was in attendance.&lt;ref&gt;&quot;Marlborough House.&quot; ''Morning Post'' 11 March 1890, Tuesday: 5 [of 8]. Col. 6b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000174%2F18900311&amp;page=5&amp;article=055&amp;stringtohighlight=mandeville+viscount. Same print title and p.
&lt;/ref&gt;&lt;/blockquote&gt;

==April 1890==
Arnold Dolmetsch took out a three-day ticket to the Reading Room in April 1890 (Campbell 22).

=== 9 April 1890, Wednesday ===

==== The New Forest United Hunt Ball ====
&lt;blockquote&gt;This annual ball was beld at the New Forest Hall, Lyndhearst, on Wednesday night, and was a most brilliant gathering, upwards of 200 being present, not only the New Forest but also neighbouring hunts being well represented. Among those present were Earl and Countess of Londesborough, Lady Mildred Denison, Lady Lilian Denison, Hon. Louis Johnstone, Hon. Gerald and Mrs Lascelles, Major Downman, Capt. Sandbach, R.H.A., Col. and Mrs Sinkins, Col. Fitzroy Smyth, Lady Thursby and party, Mr Stanley Pearce (Master of the Foxhounds), Mr F. Lovell (Master of the Deerhounds) and party, Lady Adela Goff and party, Hon. Miss St. Leger Glyn and party, Mr A. H. Jeffreys, M.P., and Mrs Jeffreys, Hon. Mrs A. Peter, Mr Somerset H. Onslow, Mr Lancelot Orde, Lord Garioch, Mr and Mrs C. K. Francis, the Countess of Normandy, Lady Mary Agar, Lord Montagu, Hon. John Scott Montagu, Viscount Cantelupe, Prince Dhuleep Singh, Hon. D. Keppel, Col. Charles Needham (1st Life Guards), [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], Mrs Cornwallis West, Mr and Mrs Shelley Bontein, Col. Gridley, Col. Newton, Col. Elliot, R.H.A., Lady Meyrick and party, Sir W. Jervois, Lady Jervois and  party, &amp;c.&lt;ref&gt;&quot;The New Forest United Hunt Ball.&quot; ''The Sportsman'' 11 April 1890, Friday: 2 [of 4], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001055/18900411/024/0002. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

==May 1890==
Leonora Braham appeared at the Opera Comique as Ruth Ferns in ''Gretna Green''.
===21 May 1890, Wednesday===
It was his pupil the young Countess Valda Gleichen who found a sponsor for Dolmetsch's first but brief appearance at a London concert on 21 May 1890, when the 'Magpie Minstrels' … gave one of their bi-annual performances at the Princes' Hall&quot; (Campbell 30).

==June 1890==

=== 3 June 1890, Tuesday ===

==== Dinner and Concert Hosted by Mrs. Arthur Williams and Ball by Mrs. Menzies ====
&lt;blockquote&gt;Yesterday evening society passed a large proportion of time on wheels, and the number of receptions was more than the most inveterate could get through wvith comfort. ... Meanwhile, the Duke of Clarence and Avondale dined with Mrs. Arthur Wilson in Grosvenor-place, and a small and select concert followed. The Duchess of Leinster was, as ever, the most beautiful among many beauties, the Hon. Helen Henniker, after her long mourning, was warmly greeted by swarms of friends, and the Countess of Lovelace, in grey satin, chaperoned her débutante niece, Miss Milbank.

Prince &quot;Eddie&quot; went from Mrs. Arthur Wilson's hospitable mansion to that of Mrs. J. Graham Menzies. It is unusual to find mother and daughter entertaining this illustrious young man on the same evening. Mrs. Menzies, who has succeeded Lord Suffield in his beautiful house in Upper Grosvenor-street, had one of the smartest and most successful balls of the present season. The Blue Hungarians played with immense vigour and owing to the postponement of Lady Carnarvon's ball, there was no competition for men and married women. Countess Howe, Lady Brougham and Vaux, Lady Aveland and Miss Willoughby, Viscountess Stormont, the Hon. Lady Grey Egerton and Miss Egerton, the Duchess of Buccleuch, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], the Earl of Craven, Countess of Coventry, Mrs. Mackay, Lady Sykes, the Marchioness of Granby, Mrs. Hwfa Williams, Lord Garioch, Sir Savile and Lady Crossley, Mr. and Mrs. Harry Lawson, and many others were present.&lt;ref&gt;&quot;Yesterday Evening Society.&quot; ''Pall Mall Gazette'' 4 June 1890, Wednesday: 4 [of 8], Col. 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18900604/015/0004. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

==== Münster-Hay Wedding ====
Account of the wedding of Count Alexander Münster and Lady Muriel Henrietta Constance Hay. Count Bismarck sent a gift.&lt;blockquote&gt;St. Andrew's Church, Wells-street, was completely filled yesterday afternoon on the occasion of the marriage of Count Alexander Münster, son of Count Münster, German Ambassador in Paris, with Lady Muriel Henrietta Constance Hay, younger daughter of the Earl and Countess of Kinnoull. The ceremony was fixed for half-past two o'clock, but all the seats in the body of the church were occupied long before that time by invited guests. The rood screen was hidden with white flowers, and a number of tall palms were skilfully arranged in and about the chancel. The bridegroom was early in his place, and wore the splendid white and gold uniform of the Garde du Corps of the Emperor; his best man, Prince Hans Heinrich Pless, wearing the scarlet and gold uniform of the Garde Hussars. The six bridesmaids were Lady Mildred Denison, Lady Dorothea Stewart Murray, Hon. Marie Hay, Hon. Marjory Murray, Miss Rosalind Lovell, and Miss Gladys Hadow (niece of the bride). They wore pretty dresses of pale blue satin, veiled with white chiffon; the skirts were edged with a frill, and the bodices finished with quaint fichus of the chiffon, fastened in front with a bunch of forget-me-nots. They wore drawn hats of the chiffon, covered with forget-me-nots, and their posies were of the same flowers, intermixed with pink roses, and tied with narrow pink ribbons. Each wore a gold bangle with centre forming the initials &quot;A.M.,&quot; and a single turquoise drop. The bride entered the church at half-past two, and was received by her father, who led her to the chancel steps, preceded by the choristers singing a nuptial hymn. The bride's dress was of ivory satin made with a very long train. The front was fringed round the hem with orange blossoms and veiled with old Brussels lace, the gift of her mother; the bodice was entirely covered with beautiful old lace, and finished at the neck on one side with a cluster of orange blossoms. She wore a small wreath of orange blossoms and myrtle arranged in the hair at the back and a tulle veil falling almost to the end of the train and held by diamond stars, the gift of the bridegroom. The bride's other jewels included two diamond drop hairpins, the gift of Count Münster; an emerald and diamond brooch, from the bridegroom; enamel and diamond heartsease brooch, from Lady Mary Mills; a diamond and emerald bracelet, from the Duke of Beaufort; and a diamond bracelet, from the Duke and Duchess of Athole. Her train was held by her two little nephews, Masters Roland and Patrick Hadow, wearing Scotch dress with lace ruffles. The service, which was fully choral, was performed by the Rev. Provost Rorison, of St. Ninian's Cathedral, Perth, assisted by the Rev. W. T. Houldsworth, rector of St. Andrew's.

The Earl and Countess of Kinnoull afterwards entertained the bridal party at the residence of the Earl of Londesborough, uncle of the bride, in Grosvenor-square. Among the numerous guests were the Russian Ambassador and Madame de Staal, the German Ambassador, the Austrian Ambassador and Countess Deym, Count Münster and the Countesses Marie, Julia, and T. Münster, Prince Pless, Prince Louis Esterhazy, Count Donhoff, Baroness von Beckendorff-Hindenburg, Baron E. Fürstenberg, Count Paul Metternich, Geheimrath Schmettau, Countess Valentin, [[Social Victorians/People/de Soveral|M. de]] [[Social Victorians/People/de Soveral|Soveral]], Captain Hasenclever, Count Leyden, Herr von Rath, Count Francis Deym, Baron and Baroness Deichmann, Count Mensdorff, Herr Pilgrim Baltazzi, Count and Countess Henry Lützow, Baroness d' Erlanger [?], Herr von Kemnitz, Baron Cramm, Vicomte de Janzé, the Duke of Beaufort, the Duchess of Athole, and the Ladies Stewart Murray, the Marchioness of Downshire, the Marchioness of Stafford and Lady Sybil St. Clair Erskine, Maria Marchioness of Ailesbury, the Countess of Dunraven and Ladies Wyndham Quin, the Countess of Kilmorey, the Countess of Galloway and Miss Stewart, the Countess of Dudley and Lady Edith Ward, the Countess of Strathmore and Lady Constance Lyon, the Earl and Countess of Roden, Lady Willoughby de Eresby and Hon. Miss Willoughby, the Countess of Westmorland. Viscount and Viscountess Raincliffe, Viscountess Coke, Viscountess Stormont and Hon. MabeI Murray, Viscountess Malden and Hon. Miss Capel, Lord Hay of Kinfauns [?], Lady Delamere and Miss Cholmondeley, Lady Brougham, Lady Esher, Lord Saye and Sele and Hon. Maud and Hon. Gertrude Fiennes, Lady Helen MacGregor and Miss MacGregor, Lord and Lady Algernon Gordon Lennox and Lady Angela St. Clair Erskine, Lady Raglan, Lord Charles Innes Ker, Lady Elizabeth Bertie, Lady Frances Pratt and Lady Clementine Pratt, Lady Geraldine Somerset, Lady Dalton Fitzgerald and Miss Payne, Lady Mary Mills and Miss Pereira, Lady Dorchester, Lady Louisa Moncreiffe and Misses Moncreiffe, Lady Norreys, Lady Petre, Lady Jane Trefusis, Lord Frederic Hamilton, Baroness de Brienen and Miss de Brienen, Helen Lady Forbes and the Misses Forbes, Lady Scott, Miss Scott and Mrs. Green, Lord Zouche and Hon. Miss Curzon, Mr. and Lady Constance Hadow, Hon. Lady Campbell, Lady William Nevill and Miss Bannerman, Hon. Alastair and Mrs. Hay, Hon. Miss Greville, Captain Hon. Randolph Stewart, Hon. FitzRoy and Mrs. Stewart, Hon. Charles Walsh, Hon. William Walsh, [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], Colonel Hon. Charles and Mrs. Hay and Miss Maude Hay, Hon. Mrs. Greville Nugent, Hon. Mrs. Colville and Miss Streatfeild [sic], Hon. Claude Hay, Sir Charles and Lady Forbes of Newe, Laely Borthwick, Sir Francis Montefiore, Sir Henry Hoare, Sir George Arthur, Sir William Gordon Cumming, General and Mrs. Wilkinson, Colonel and Mrs. Chaine, Colonel Arthur Paget, Colonel H. M. Hozier, the Provost of St. Ninian's, Major Finch, Major Candy, Colonel Lloyd, Captain and Mrs. Stewart, Mr. and Mrs. Hay Drummond, Captain and Mrs. Lloyd, Mr. William Gillett, Mr. Hulse, M.P., and Mrs. Hulse, Captain Lumley, Captain Barrow, Major Anstruther, Mrs. Hwfa Williams, Mr. Arthur Hay, Mr. Raglan Somerset, Mr. and Mrs. George Cavendish Bentinck, Mrs. Villiers, Mr. Henry Petre, Mrs. Keighley, Mrs. E. Balfour and Miss Balfour and Miss Ellice, Mrs. Dick Cunynghame and Miss A. M'Gregor, Rev. C. Weidemann, Miss Balfour and Miss E. Balfour, Mrs. and Miss Halford, Mr. and Mrs. Toler, Mrs. and Miss Townley, Rev. Dr. M'Ewan, Mr. A. F. Levita, Mr. F. Stephens, Mrs. and Miss Leigh, Mr. and Mrs. George Forbes and Miss Forbes, Mrs. Luke Wheeler, Mrs. J. Beerbohm, Dr. and Mrs. W. M. Collins, Mrs. and Miss Orde, Mrs. Murray, Miss Glyn, Mrs. Godfrey Pearse, Mr. Balfour, Mr. Leopold Goldberg, Mr. and Miss Oswa d [Oswald], Mr. and Mrs. C. Bulteel, Mrs. Brydges Wyllyams, Mr. H. Balfour, the Misses Codrington, Miss Finch, Mrs. Barron and Miss Sullivan, Mr. Hamilton Aidé, Mr. Granville and Miss Berkeley, Mr. M'Gregor, Mrs. and Miss Needham, Mr. and Mrs. A. Consett and Miss Consett, Mrs. Herbert Naylor LeyIand, Mr. and Mrs. A. Darby, Mrs. Montefiore, Mrs. Charles Murray and Miss Murray, Mrs. Thomas Legh, the Rev. John F. Mitchell, Mr. and Mrs. Claud Hay, Mr. Fiztalan Manners, Mr. Albert Stopford, Mr. Hervey Pechell, and Mr. and Mrs. Charles Orde.

Later in the day Count Alexander Münster and his bride left for Hillingdon Court, Uxbridge, the residence of the Hon. A. Mills, where they will pass the early days of the honeymoon, and then proceed to Chàlet Sans Souci, Bellaggio, Lake of Como, lent by Mr. Hervey Pechell. They will afterwards go to Wiesbaden, and thence to Count Münster's German country seat, where a great reception awaits them.

The wedding presents were very numerous. Count Munster presented the bride with a diamond necklace and pair of diamond drop hairpins. The bridegroom's gifts to his bride included a tiara of three diamond stars, a brooch formed of an emerald of unusual size set in diamonds, large pearl pendant, gold bracelet set with turquoises, and diamond and turquoise ring. The Duke of Beaufort presented Lady Muriel with an emerald and diamond bracelet. The Earl and Countess of Kinnoull's presents included a quantity of plate and other articles. Prince Henry of Battenberg sent a large silver-mounted claret jug; Count Bismarck, a silver box; the Marchioness of Waterford, gold snake bracelet, with pearl head and ruby eyes; the Duke and Duchess of Athole, diamond &quot;M&quot; bangle; Lady Ermyntrude Malet, massive silver bowl; Countess Marie Münster, silver tea set and tray; Baron E. Fürstenberg, pair of gold-mounted claret jugs; Baron and Baroness Erlanger, large silver bowl; Baron and Baroness Gungberg, pair of antique silver mounted jugs.&lt;ref&gt;&quot;Marriage of Count Alexander Münster and Lady Muriel Hay.&quot; ''Morning Post'' 4 June 1890, Wednesday: 7 [of 12], Col. 7a–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18900604/064/0007. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

===4 June 1890, Wednesday===
Derby Day.

According to the Morning Post, &lt;quote&gt;Lady Thurlow's first dance. / Mrs. Coddington's Ball. / The Fourth of June celebration at Eton. / ... Royal Society of Literature — Paper on &quot;Early England,&quot; by Mr. Carmichael, S. &lt;/quote&gt; (&quot;Arrangements for This Day.&quot; The Morning Post Wednesday, 4 June 1890: p. 7 [of 12], Col. 6A).

===13 June 1890, Friday===
? or on the 12th? Arnold Dolmetsch had a concert at which his students performed (Campbell 31). It was reviewed very positively in the 13 June Daily Graphic, especially Helene Dolmetsch's performance. They did Purcell's Fairy Queen. They used a harpsichord.

===26 June 1890, Thursday===
There was apparently a regular celebration of [[Social Victorians/People/Arthur Collins|Arthur Collins]]' birthday, 26 June, by Bret Harte, George Du Maurier, [[Social Victorians/People/Arthur Sullivan|Arthur Sullivan]], Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

==July 1890==
===3 July 1890, Thursday===
&lt;blockquote&gt;On July 3, 1890, Besant’s house at 19 Avenue Road, St. John’s Wood, was inaugurated as a new center of Theosophical work, serving as the European headquarters of the [[Social Victorians/Theosophical Society|Theosophical Society]] and as HPB’s residence. That house became also the meeting place of HPB’s Inner Group, twelve of her students who were eager for more intense training than was feasible in a larger, more general gathering.&lt;/blockquote&gt;That Inner Group is different from the Esoteric Section.&lt;ref&gt;&quot;Esoteric World Chapter 23.&quot; ''The Theosophical Society of America, Online Resources''. http://www.theosophical.org/index.php?option=com_content&amp;view=article&amp;catid=23&amp;id=1725&amp;Itemid=53&lt;/ref&gt;&lt;blockquote&gt;The hall had a seating capacity of about 200. On the opening night [July 3, 1890] [sic] the room was crammed, and many were unable to gain admission. The speakers were Mrs. Besant, Mr. Sinnett, a Mrs. Woolff (of America), and Mr. [Bertram] Keightley. HPB was present but said nothing, on account of the critical state of her health.&lt;ref&gt;&quot;23a. Henry S. Olcott, July 1890, London [Olcott 1931, 4:254–6].&quot; Esoteric World Chapter 23. ''The Theosophical Society of America, Online Resources''. http://www.theosophical.org/index.php?option=com_content&amp;view=article&amp;catid=23&amp;id=1725&amp;Itemid=53.&lt;/ref&gt;&lt;/blockquote&gt;

=== 4 July 1890, Friday, 11 p.m. ===

==== The Queen's State Ball at Buckingham Palace ====
The Prince and Princess of Wales were hosts of this ball, as Queen Victoria was not present. Many of the Queen's children and their spouses were present.&lt;ref&gt;&quot;State Ball at Buckingham Palace.&quot; ''Morning Post'' 5 July 1890, Saturday: 5 [of 8], Col. 5a–7b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18900705/038/0005. Same print title and p.&lt;/ref&gt; The dancing commenced shortly after the Prince and Princess of Wales arrived at 11:00.

=== 1890 July 15, Tuesday ===

==== Garden Party at Marlborough House to Meet the Queen ====
The beginning of the ''Morning Post'' article, which is followed by a very long list of people invited:&lt;blockquote&gt;Their Royal Highnesses the Prince and Princess of Wales gave a garden party at Marlborough House yesterday afternoon to meet the Queen.

Her Majesty was accompanied by their Royal Highnesses the Princesses Victoria and Margaret of Prussia, and was attended by the Duchess of Roxburghe, Miss M'Neill, the Hon. Evelyn Moore, the Hon. Bertha Lambert, and Major-General Sir Henry Ewart and Major F. A. Bigge. Madlle. De Perpigna was in attendance on the Princesses Victoria and Margaret.

The following were present: — Their Royal Highnesses the Duke and Duchess of Edinburgh and Prince Alfred, and the Princesses Marie, Victoria, Alexandra, and Beatrice of Edinburgh; their Royal Highnesses the Duke and Duchess of Connaught and Prince Arthur, and the Princesses Margaret and Patricia of Connaught; their Royal Highnesses the Prince and Princess Christian of Schleswig-Holstein Sonderburg-Augustenburg and Princess Victoria and Princess Louisa of Schleswig-Holstein, her Royal Highness the Princess Louise, Marchioness of Lorne, and the Marquis of Lorne.

Her Royal Highness the Duchess of Albany, her Royal Highness the Princess Frederica and the Baron von Pawell-Rammingen, his Royal Highness the Duke of Cambridge, her Royal Highness Princess Mary Adelaide Duchess of Teck and his Highness the Duke of Teck and Princess Victoria of Teck, his Royal Highness the Duke d'Orleans and Princess Hélène d'Orleans, his Imperial Highness Don Pedro Augustus of Coburg and Braganza, his Serene Highness the Prince of Schaumburg-Lippe, his Serene Highness the Prince of Leiningen and their Serene Highnesses Prince and Princess Victor of Hohenlohe-Langenburg and the Countesses Gleichen, and Count Gleichen.&lt;ref&gt;&quot;Garden Party at Marlborough House.&quot; ''Morning Post'' 15 July 1890, Tuesday: 5 [of 8], Col. 3a–7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18900715/044/0005. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

=== 19 July 1890, Saturday ===

==== Wedding of James Francis Harry St. Clair-Erskine and Violet Aline Vyner ====
This report from the ''Fife Free Press'' is missing a big piece of the 2nd paragraph, where the bridesmaids' and bride's dresses are described, because the page was damaged. The digitized copy is also generally poor.&lt;blockquote&gt;On Saturday forenoon, in Michael’s Church, Chester Square, London, was celebrated the marriage of Lord Loughhorough, eldest son of the Earl of Rosslyn with Miss Violet Aline Vyner, younger daughter of Mr R. C. Vyner, of Fairfield, Yorkshire. The chancel was beautifully decorated with palms and a profusion of lilies most artistically arranged. The Prince of Wales, Duke of Cambridge. Princess Mary Adelaide, Duchess and the Duke of Teck, and Princess Victoria, and the Right Hon. W. E. Gladstone were among those present.

The wedding party began to arrive at 11 o’clock, the bridesmaids being early in attendance. They were the Ladies Sybil and Angela St Clair Erskine, sisters of the bridegroom; Lady Anne Lambton, Miss Musgrave, Miss Rachel Gurney, and Miss Fleming. They were charmingly dressed in soft cream crepon, with violet velvet Zoave jackets, forming half sleeves and capes at the back, and pretty turn-down collars and cravats of white mosseline [mousseline?] chiffon, and the skirts were very plainly made. They wore large white hats lined with a band of violet velvet near the face, and trimmed on the crown with white ostrich plumes, a bunch of violets fastening the brim at the back. Each wore a brooch — the St Clair cross in rubies and diamonds set in a circle of the latter, and surmounted by a baron’s cornet of the same precious stones — the gift of the bri[degroom]; and carried a bouquet of Marechal Niel [roses?] ...ging sprays of the same, and tied w... ribbons. The bride entered the ... eleven o’clock, being received at ... father, who led her to the cha... her away. The service be... procession was preceded up ... choir, who sang &quot;The voic...&quot; The bride’s dress was ... with a long court train, ... white velvet being embro... ...und the train, and fasten... ...ver true lover’s knot. The picture... ...gh silver waistband, had full slee... mousseline chiffon; and a small ... blossoms was most becomingly arra... with a long tulle veil. The Earl of Chesterfield discharged the duties of best man.

The Rev. Canon Fleming, Chaplain in Ordinary to the Queen and Vicar of St Michael's, performed the marriage rite, assisted by the Rev. Edgar Sheppard, Sub-Dean of the Chapels Royal, and the Rev. J. Thomson, of Rosslyn, near Edinburgh. The hymn “Thine for ever! For of love,” was sung the end of the service. Canon Fleming afterwards delivered a most impressive address. After the benediction the clergy and bride and bridegroom passed to the vestry, the Prince of Wales following with Mrs Vyner. Pretty wedding favours of orange blossoms, Parma violets, and white heather were then distributed amongst the congregation.

Mr and Mrs Vyner afterwards welcomed the wedding party at Ashburnham House, Dover-street. The ''dejeuner'' was served in three rooms, one being reserved for the bride and bridegroom and the Royal party. The table in the latter room was decorated with several of Mr Vynet's racing trophies. The band of the Grenadier Guards performed in the garden during the reception. The Prince of Wales, Duke of Cambridge, the Duke and Duchess of Teck and Princess Victoria were present at the breakfast, and among the general company were Count Munster and Countess Maria Munster, the Marchese and Marchesa de Montagliari, the Marquis and Marchioness of Ripon, the Marquis and Marchioness of Stafford, the Marquis of Cholmondeley, the Marquis of Northampton, Maria Marchioness of Ailesbury, the Dowager Marchioness of Conyngham and Lady Blanche Conyngham, the Marchioness of Downshire, the Countess of Rosslyn, Earl and Countess Compton, the Earl of Feversham, the Earl of Durham, the Countess of Coventry and the Ladies Coventry, Countess Howe and Ladies Curzon, the Countess of Yarborough, the Earl of Clonmell, the Earl and Countess of Loudoun, the Countess of Kilmorey, Countess de Grey, Viscount Molyneux, the Bishop of Gibraltar and Mrs Sandford, Viscountess de Labrosse and Mdles. de Labrosse, Lord Greenock, Lord and Lady Algernon Lennox, Lady Lilian Wemyss, Lady Julia Wombwell and Miss Wombwell, Hon. Lady Campbell of Blythswood, Lady Constance Harris, Lady Florence Harris, Lord and Lady Burghley, Lady Dorchester, Lord Houghton, Lady Curzon, Lady Brougham and Vaux and Miss Musgrave, Baron de Hirsch, Helen Lady Forbes and the Misses Forbes, Baroness Burdett Coutts and Mr Burdett Coutts, M.P., Lady Astley, Lord and Lady William Nevill, Lord and Lady Brooke and Hon. Leopold and Hon. Marjorie Greville, Lady Dalton Fitzgerald and Miss Payne, Lord Elcho, Lady Willoughby de Eresby and the Misses Willoughby, Lady Ewart, Lady Hindlip, Lady Cecilia Rose, Lord Rowton, Lord Capell, Lady Mabel Compton, Lord and Lady Herries, Lady Sykes, Lord and Lady Alwyne Compton, Lady Ventry and Hon. Miss de Moleyns, Hon. Lady Knollys, Lady Manners, Hon. Lady Drummond and Misses Drummond, Hon. Sydney Greville, Hon. Assheton Harbord, Hon. Derek Keppel, Hon. Captain Bourke, Hon. Mrs Percy Mitford, Hon. Philip Harbord, Hon. and Rev. L. Tyrwhitt, Hon. Coralie Glyn, Hon. M. Lambton, Hon L. Greville, Hon. Alwyn Greville, Hon[.] Eva Greville, Hon. Frances Dawnay, Hon Evelyn Paget, Hon Mrs Algernon Grosvcnor, Hon and Mrs Lambton. Hon. Mrs Evelyn Pelham, Hon. Fitzroy St Clair Erskine, [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], Hon. W. Maxwell, Hon. G. and Mrs Dawnay, Hon. Captain Lambton, General Sir Seymour Blane, Sir William Gordon Cumming, Sir Archibald and Miss Edmunstone, Sir Henry and Lady Meysey Thompson, Mrs Gladstone, Mr and Lady Margaret Cameron, Mr and Lady Florence Astley, Mr and Lady Elizabeth Melville Cartwright and Miss Melville Cartwright, General and Mrs Duff and Miss Duff, General Owen Williams, Colonel and Mrs Anstruther Thompson, Colonel Stopford Sackville, Colonel Craig, Colonel Brabazon, Colonel Forester, Colonel Stanley Clarke (in attendance on the Prince of Wales) and Miss Clarke, Major Davidson, Canon and Mrs Fleming, Captain St John Mildmay (in attendance on the Duke of Cambridge), Captain and Mrs FitzGeorge, Mrs William Portal, the Sub Dean of the Chapels Royal, Rev. W. M. and Mrs Wollaston, Rev. R. West, Mr and Miss Chamberlain. Mr and Mrs W. H. Grenfell, Mr Christopher Sykes, M.P., Mr Reuben Sassoon, Mr Arthur Sassoon, Mrs Bischoffsheim, Mr and Mrs Herbert Naylor Leyland, Dr and Mrs Anderson, Mrs Oswald, Mr and Mrs Surtees, Mr Fitzgerald, Mr and Mrs Menzies, Miss Willoughby and Miss Gertrude Willoughby, Mr Arthur Paget, Miss Christie, Mr Dowdall, Mrs Eastwood and the Misses Eastwood, Mr Frederick Warre, Mr William Williamson, Mrs Burton, Mrs Chaine, Captain and Mrs Livesey Wardle, Captain A. R. Hill, Miss Helby, Mrs and Miss Winslow, Mr and Miss Oswald, Mr Willoughby, Mr Quintin Hume, Mr F and Miss Fitzherbert, Mrs and Miss F. Hotham, Mr and Mrs Moreton Frewin, Mrs Charles Otway, Mr Calcraft, Mr Watson, Mr Fennick, Mr Montgomery, Mr Cecil Murray, Mr and Mrs Sneyd, Mr Leslie Stephen, Mr Edgar Sebright, Miss Fleetwood Wilson, Mrs and Miss Farmer of Nonsuch, Mr and Mrs Dennistoun and Miss Dennistoun, Mr and Mrs J. R. Lane Fox and Miss Lane Fox, &amp;c. 

The bride and bridegroom left early in the afternoon for Easton Lodge, Dunmow, the seat of Lord and Lady Brooke, in Essex, where they will spend the honeymoon. The bride travelled in a costume of biscuit coloured armure silk, the top of the bodice and sleeves being of pale pink mousseline de soie, and the lower part of the former inserted with pink velvet ribbons to form a high band, Tuscan straw-hat trimmed with pink crepe de chine, and biscuit feathers. The presents exceeded four hundred in number. The Prince of Wales presented the bride with a trefoil moonstone and diamond brooch and the bridegroom with a sapphire and diamond pin. The Princess of Wales's gift the bridegroom was a silver-necked claret jug. The Duke of Cambridge gave an amethyst and diamond pendant, and the bridegroom a pair of silver gilt candlesticks; and Princess Mary and the Duke of Teck presented the bride with a silver sugar basin. The bridegroom’s gifts to the bride were a diamond and sapphire watch bracelet, a diamond half-hoop ring, diamond brooch with pearl centre, diamond and turquoise brooch, formed of the St Clair badge in rubies and diamonds set in a circle of diamonds, surmounted by a baron’s coronet in the same precious stones, a large salts bottle with two heart-shaped moonstones set with rubies and diamonds and a silver sugar basin. The bride presented Lord Loughborough with a turquoise and diamond stud. The Earl of Rosslyn presented the bride with diamond necklet. The Countess of Rosslyn’s gifts were diamond orchid brooch and a pink feather fan. Mr R. C. Vyner’s gifts to his daughter were a diamond and pearl tiara and gold mounted dressing case, and Mrs Vyner gave her a sapphire and diamond ring. The Marchioness of Stafford gave a ruby and diamond pin; Lady Mary Vyner antique diamond tiara; the Ladies Angela and Sybil Erskine sapphire and diamond bracelet; Hon. Fitzroy St Clair Erskine with &quot;1890&quot; in rubies and diamonds; Lord and Lady A. Compton large diamond star; the Earl of Rosslyn presented his son with a large silver bowl and two silver dishes; the Countess of Rosslyn's present was a travelling bag; Mr Vyner gave him a luncheon basket; Mrs Vyner a silver ''entree'' dish; the Marchioness of Stafford case containing silver coffee and tea pots, urn and stand, sugar basin, and cream jug; Lord and Lady Brooke four antique silver sauce boats; Lord and Lady Algernon Gordon ['''Col. 1c–2a'''] Lennox three antique silver ''entree'' dishes. The Earl of Rosslyn's Fifeshire tenants presented Lord Loughborough with a beautiful antique silver bowl, two antique silver dessert dishes, and two antique sugar castors; and to the bride they gave an antique silver tea service. The congregation of Rosslyn Chapel presented the bridegroom with a complete and elegant writing set, whilst Lord Rosslyn's servants gave him a silver inkstand and pair of silver candlesticks. Mr Vyner's servants presented the bride with a silver salver and six ''liqueur'' cups. The servants of Newby Hall gave a silver coffee pot, and Mr Vyner’s Cheshire tenants presented a case containing silver tea pot, sugar basin, and cream jug. The bride also received from the Duchess of Portland a travelling bag; the Duchess de Luynes, sapphire and diamond ring; the Duke of Westminister, Indian necklace; the Marquis of Northampton, diamond bracelet; the Marquis of Ripon, sapphire and diamond bracelet; the Marchioness of Ripon, turquoise and diamond bangle, the Earl of Durham, a diamond half hoop bracelet; Earl and Countess Cowper, a diamond &quot;V V” brooch; Dowager Viscountess Downe, moonstone and diamond crescent; Lady Skyes [Sykes] ruby and diamond fish brooch; Lady Millbank, sapphire and diamond brooch Lord Douglas Compton, double heart brooch; Lord Herbert Vane Tempest, gold curb chain bracelet set with pearls; Earl and Countess Compton, bangle with “Vi” and “good luck” on it; the Duke and Duchess of St Albans, tea service with table; the Marchioness Conyngham, silver cream jug; the Marchioness of Tavistock, silver vase; the Countess of Rodin, a silver I bowl; the Countess of Yarborough, silver candlesticks; Viscountess Downe, silver tea caddie; Lady de Trafford, gold mounted salts bottle; the Hon. F. Dawnay, large silver candlesticks[;] Hon. F and Lady Lampton, travelling clock; Hon. W. Lambton, silver candlesticks; Sir R. and Lady Graham, silver salver; Sir Roderick and Miss Cameron, two silver dishes; General Williams, diamond bangle; Colonel and Mrs G. FitzGeorge, gold mounted bottle; Major and Mrs Egerton, pair of silver candlesticks; Major Stuart Wortley, diamond Swallow; Major Davidson, heart-shaped brooch in coral and diamonds; Captain and Lady Cecilia Rose, a brougham; Mr Beaumont, silver bowl; Miss Edmonstone, moonstone and diamond hat pins; Mrs Harris, sapphire and diamond bracelet; Mr Egerton, turquoise and diamond brooch; Sir Cecil Murray, sapphire and diamond pin; Mr A. Farquharson, diamond swallow brooch; Mr and Mrs Hulse, two small silver vases; Miss Fleetwood Wilson, diamond bangle; Mrs A. Wilson, tortoiseshell candlestick; Mr Quintin Hume, salts bottle mounted with diamonds and rubies; Miss Helbert, gold violet pin; Mr Chamberlain, pair of silver candlesticks; Hon. Arthur Coventry, gold mounted bottle with &quot;Vi&quot; in diamonds; Mrs Leopold de Rothschild, diamond hand brooch, together with a number of other gifts. Among the presents to the bridegroom were — from the Marchioness of Downshire, antique silver sugar sifter; the Marquis of Exeter, silver sandwich case; the Marchioness of Bath, antique Dutch silver box; the Marquis of Downshire, a gold pencil; Count Munster, cigarette case and match box; Count Alexander Munster, a hunting flask; the Countess of Lindsay, antique silver pen-tray; the Earl of Mar and Kellie, silver matchbox; the Earl and Countess of Loudoun, silver cigarette box; the Earl of Chesterfield, antique silver gilt inkstand; the Countess of Bradford, gold seal with agate; the Countess of Warwick, antique silver bowl; the Earl of Coventry, silver pen-tray; the Countess of Wharncliffe, two silver candlesticks; the Earl and Countess of Cromartie, two antique silver cups; Viscountess of Newport, silver paper knife; Mr and Mrs A. Sassoon, ruby and diamond pin; Lord John Cecil, silver salver; Lord and Lady Willoughby de Eresby, antique silver-mounted cruet stand; Lord William Nevtll, antique brandy carrier; Lady Margaret Spicer, silver match box; Lord Burghley, four silver salt cellars and spoons; Baron de Hirch [Hirsch?], silver inkstand; Lady W. E. Osborne Elphinstone, silver inkstand; Lord Kesteven, silver cream jug; Lord Capell, silver cigarette case; Lord and Lady Gerard, tortoiseshell and silver travelling clock; Lady Lilian Wemyss, silver cigarette case; Dad Alwyne Compton, umbrella containing matchbox and whistle; Lord and Lady Lennox, two antique silver ''entree'' dishes and bacon dish; Lord Burghersh, silver cigarette lighter; Lady Angela 8t Clair Erskine, four silver salt cellars; Lady Randolph Churchill, gold pencil case, with two sapphires; Lord Houghton, antique gold basket; Lady Sybil St Clair Erskine, umbrella; Lord and Lady Dorchester, large crystal seal; Hon. Derek P. Keppel, pair of silver candlesticks; Hon. E. and Mrs Pelham, silver inkstand; Hon. G. N. Curzon, silver gilt bowl; Hon. F. St Clair Erskine, four silver candle-sticks; [[Social Victorians/People/Bourke|Hon. A. and Mrs Bourke]], four small silver dessert dishes; Hon. Mrs Elliot Yorke, pair of silver candlesticks; Hon. Mr and Mrs L. Greville, tortoise-shell and silver box; Hon. R Somerset, diamond and pearl pin; Hon. G. H. Willoughby, silver ink-stand; Hon. H. and Mrs Grosvenor, umbrella; [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], enamel and diamond pin; Captain Hon. Maurice Bourke, cigarette case and lighter; Hon. W. Maxwell, silver-backed clothes and hat brushes; Hon. Sidney Greville, saltspoons; Hon. M. C. Maxwell Scott, two silver ''menu'' plates; Hon. W. Edwardes, pin; [[Social Victorians/People/Greville|Captain Hon. A.]] and [[Social Victorians/People/Lady Violet Greville|Mrs Greville]], silver gilt bowl, fork, spoon, and ladle; Sir Frederick Milner, diamond and moonstone pin; Sir George Chetwynd, two long silver flagons; Sir M. and Lady Fitzgerald, two silver saltspoons; Sir N. Gordon Gumming, silver-handled paper knife, &amp;c.&lt;ref&gt;&quot;Marriage of Lord Loughborough with Miss Vyner.&quot; ''Fife Free Press'' 26 July 1890, Saturday: 2 [of 8], Col. 1a–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001110/18900726/015/0002. Same print title and p.&lt;/ref&gt; &lt;/blockquote&gt;

=== 24 July 1890, Thursday ===

==== Dinner and Dance Hosted by Lord Alington ====
Perhaps the date on this is uncertain, since the article in ''Truth'' would suggest it was held in late May or early June. The newspaper story in the ''Queen'' mentions another occasion in which the flowers were notable as well.

From ''Truth'':&lt;blockquote&gt;
But not a quarter of a mile distant [from a dinner and dance hosted by Lord Rothschild featuring Princess Louise and the Marquis of Lorne] a more important event was proceeding, for Lord Alington, having previously walked down the Row and invited his friends right and left to Alington House, South Audley-street, proceeded to give a dance which was honoured by the presence of the Prince and Princess of Wales, the Princesses Victoria and Maud, the Duke of Clarence, Princess Mary Adelaide, and Princess &quot;May&quot; and Prince and Princess Christian. This without exaggeration, with the exception of Lady Leconfield's, Lady Willoughby de Eresby's, and Lady Cadogan's, was the best ball hitherto given this season, and the prolific way ortolans [small songbirds regarded as a delicacy] were distributed at supper will long linger in the memories of those by whom these delicacies are cherished. One lady displayed her enthusiastic appreciation by devouring five of these, and it is to be hoped her devotion did not endanger her life. As for beauty, seldom before have so many pre-eminent for good looks been present at one gathering, as a mere enumeration of a few of these will prove. Of course the Duchess of Leinster heads the list, followed in quick succession by the Duchess of Portland, Lady de Grey, Lady Randolph Churchill, Lady Dudley, Lady Kilmorey, Lady Brooke, Lady de Trafford, Lady Helen Duncombe, Lady Hilda Dundas, Lady Sybil St. Clair Erskine, Lady Olivia Taylour, Miss Rachael Gurney, Lady Cardross, Miss Bourke, Lady Rose Leigh and her sister-in-law, Miss Leigh, Miss Berens (sister to Lady Cairns), Mrs. Ralph Sneyd, Lady Gerard, and a host of others far too numerous to mention. I often wonder that no painter has yet attempted to give us in one picture a permanent record of the chief beauties of our day. It would make a most interesting and exquisite group of lovely women, such as could not be found probably in any other country than this.&lt;ref&gt;Marmaduke, pseud. &quot;Letters from the Linkman.&quot; ''Truth'' 12 June 1890, Thursday: 26 [of 56], Col. 1a–b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18900612/064/0026. Same print title, p. 1212.&lt;/ref&gt;&lt;/blockquote&gt;
From the ''Queen'':&lt;blockquote&gt;The P&lt;small&gt;RINCE AND&lt;/small&gt; P&lt;small&gt;RINCESS OF&lt;/small&gt; W&lt;small&gt;ALES&lt;/small&gt; and the Princesses Victoria and Maud honoured L&lt;small&gt;ORD&lt;/small&gt; A&lt;small&gt;LINGTON&lt;/small&gt; by their presence at D&lt;small&gt;INNER&lt;/small&gt;, at A&lt;small&gt;LINGTON&lt;/small&gt; H&lt;small&gt;OUSE&lt;/small&gt;, South Audley-street, on the 24th ult., when a distinguished party was present to meet them, including, among others, the Duke and Duchess of Leinster, the Marquis of Hartington, the Marquis and Marchioness of Ormonde, Maria Marchioness of Ailesbury, Earl and Countess Cadogan and Lady Emily Cadogan, the Earl Countess of Lucan and Lady Rosaline Bingham, the Earl  of Hardwicke, the Countess of Dudley and Lady Edith Ward, the EarI of Chesterfield, the Earl of Stradbroke and Lady Hilda Rous, and Earl Annesley. Covers were laid for sixty. Lord Alington afterwards gave a dance to meet the Prince and Princess of Wales and their daughters. As on the previous occasion, the floral decorations were exquisite. The entrance hall and the approaches to the reception rooms were decorated with tall palms and a profusion of lilies, pelargoniums, ferns in every variety, and roses in every imaginable shade. The conservatories at the back were carpeted and furnished luxuriously, and blocks of ice, lighted by fairy lamps, were placed about with artistic effect, serving to keep the atmosphere cool and fresh. Feathery palms, hydrangeos [hydrangeas] and arums were here used freely, and a particularly pretty result was obtained by the windows being framed, one in a fringe of ferns and red pelargoniums, and the other in ferns and fuschias. The ballroom fireplaces were adorned on each side with palms reaching to the ceiling, the mantelpieces being hidden by a delicate arrangement of roses in various shades springing from banks of hydrangeas, calceolarias, pelargoniums, and marguerites, and the walls of the staircase leading from the conservatory to the ball-room were hung with half-balls of floral roses. The supper was served in the dining-room, the tables being embellished with the loveliest orchids and roses of the most delicate tints, intermixed with pancretia; the arrangement was so light and elegant that it was difficult to believe that hands had ever touched the flowers. On those tables with silver candelabra in the centre, the flowers were all pure white, and those having gold candelabra were treated with mauve orchids and the palest pink and yellow roses. A tent, arranged near the conservatory for the Prince of Wales, was draped with Oriental hangings, and outside were groups of flowers and myriads of fairy lamps. The company began to arrive at eleven o'clock, when dancing commenced to the strains of the Blue Hungarian Band. The Princess of Wales was dressed in white striped satin and silk, the front being embroidered in pale shades, and wore handsome diamond ornaments. The Princesses Victoria and Maud wore white tulle over satin, the front being sprinkled all over with tiny sprays of lilies of the valley, each laid on a single leaf. The Duchess of Wellington was in black satin, with a pink sash arranged very prettily across the back of the bodice, and falling to the feet; a cluster of pink flowers and a beautiful diamond spray were fastened in the front of the bodicea and a diamond rivière was arranged in the hair, a diamond necklace being also worn. The Duchess of Westminster was in white satin trimmed with gold embroidery, and veiled in white chiffon. The Marchioness of Ormonde wore white striped brocade and satin trimmed with white lace, and a splendid diamond tiara and other ornaments. Countess de Grey, palest blue satin, with front beautifully embroidered in beads, and a diamond and pearl coronet. Maria, Marchioness of Ailesbury, white brocade and lace, with splendid diamond and emerald ornaments. The Marchioness of Bath, cream an violet brocaded velvet, the front being covered with mauve [38, Col. 3c – 39, Col. 1a] violets. Lady Mary Mills, rose-pink satin, with front richly embroidered; Lady Cardross, white satin, trimmed round the bodice and train with silver embroidery; Lady William Nevill, pale yellow brocade, the front veiled with black net, trimmed up the side with jet leaves, and all round the skirt was a bordering of Maréchal Niel roses, over a flounce of black net; Countess Granville wore rich white brocade and beautiful jewels; the Countess of Sefton, black satin and diamonds; Viscountess Dungan, white mousseline de soie, the skirt edged with a deep flounce; Lady Brooke, pale blue satin, trimmed with silver; Lady Emma Crichton, white satin train, with front of white lisse, prettily embroidered in red; Lady Idina Brassey, pale mauve bengaline, with front of chiffon and a handsome diamon coronet; Lady Rose Molyneux, white cross crêpe de Chine, with a pale green sash, and prettily trimmed with pink roses; Lady Wimborne, pale grey satin; the Hon. Miss Guest, pink satin, veiled with white net, sparkling with silver; Lady Sarah Spencer Churchill, white satin, with a chiffon frill; Lady Chesham, white silk, with pink roses; the Countess of Normanton, pale grey satin, with front of fine old lace; Mrs Hulse, handsome white brocade, diamond tiara, &amp;c.; Mrs Bischoffsheim, white silk, embroidered with silver, and trimmed round the bottom of the skirt and train with a ruche of pale yellow crèpe; the Hon. Muriel Brassey, white chiffon, over satin, slightly trimmed with pink; and the [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]] was in pink, with magnificent diamonds.&lt;ref&gt;&quot;Entertainments, Balls, &amp;c.&quot; ''The Queen'' 2 August 1890, Saturday: 38, Col. 3c – 39 [of 82], Col. 1a–1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002627/18900802/237/0038 and https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18900802/237/0039. Print: ''The Queen, The Lady's Newspaper'', pp. 170–171.&lt;/ref&gt;&lt;/blockquote&gt;This is the story from the ''Morning Post'':&lt;blockquote&gt;The Prince and Princess of Wales and the Princesses Victoria and Maud honoured Lord Alington by their company at dinner last evening at Alington House, South Audley-street. The guests present to meet their Royal Highnesses comprised the Duke and Duchess of Leinster, the Marquis of Hartington, the Marquis and Marchioness of Ormonde, Maria Marchioness of Ailesbury, Earl and Countess Cadogan and Lady Emily Cadogan, the Earl and Countess of Lucan and Lady Rosaline Bingham, the Earl of Hardwicke, the Countess of Dudley and Lady Edith Ward, the Earl of Chesterfield, Earl Annesley, the Earl of Stradbroke and Lady Hilda Rous, Lord and Lady Gerard, Lady Norreys, Lord Rowton, Lord Calthorpe, Lord Frederick Hamilton, Lord Charles Montagu, Lord Herbert Vane Tempest, Lord Arthur Grosvenor, Lady Lilian Wemyss, Colonel the Hon. Oliver Montagu, Sir John and Lady Lister Kaye, the Hon. Humphrey and Lady Feodore Sturt, the Hon. John Baring, the Hon. Henry and the Hon. Julia Stonor, the Hon. Gilbert Willoughby, Lady Suffield and Major-General Ellis, in waiting on the Prince and Princess of Wales; Sir Henry Calcraft, Mr. and Lady Rose Leigh, General and Mrs. Owen Williams, Mr. Mildmay, M.P., Mr. and Mrs. Arthur Sassoon, Mr. Montague Guest, Captain Orr-Ewing, Mrs. Bulkeley, Mr. Ricardo, and Mr. Caryl Craven.

Lord Alington afterwards gave a dance expressly to meet the Prince and Princess of Wales.

Among the company were— The Russian Ambassador, the Danish Minister, Prince Louis Esterhazy, Comte Costa de Beaunyardt, the Duchess of Buccleuch and Lady Evelyn Fitzmaurice, the Duchess of Westminster, the Dowager Duchess of Marlborough and Lady Sarah Spencer Churchill, the Duchess of Wellington and Lady Cardross, the Marquis and Marchioness of Granby and Miss Bourke, the Marchioness of Stafford and Lady Sybil St. Clair Erskine, the Marchioness of Bath and Lady Beatrice Thynne, the Marquis of Cholmondeley, the Marquese and Marquesa de Santurce and Lady Wilham Nevill, Countess Spencer, Countess Granville and Lady Victoria Leveson-Gower, Countess de Grey, the Earl of Dunraven, the Countess of Lathom and Lady Edith Wilbraham, the Countess of Enniskillen and Lady Christian Cole, the Earl of Ilchester, the Earl of Durham and Lady Anne Lambton, the Earl of Dalkeith and Lord Ernest Scott, the Countess of Sefton and Lady Rose Molyneux, Countess Howe and the Ladies Curzon, the Countess of Normanton and Lady Mary Agar and Miss Mary Liddell, Earl Craven, Viscount Clifden, Viscount Ennismore and Lady Beatrice Hare, Viscount Coke and the Hon. Violet White, Viscount and Viscountess Castlerosse and the Hon. Susan Baring, Viscountess Newport and the Hon. Miss Bruce, Viscount and Viscountess Melgund, Viscount and Viscountess Curzon, Viscount and Lady Violet Dangan and Lady Eva Wellesley, Viscount Dungarvan, Viscount Chelsea, Viscount Royston, Lady Hastings, Lord Capell, Lord and Lady Willoughby de Eresby and Hon. Margaret Willoughby, Lady Cloncurry and Hon. Miss Winn, Lord and Lady Brooke, Lady Wimborne and Hon. Miss Guest, Lord Sandhurst, Lord and Lady Edmund Talbot, Lord and Lady Alwyne Compton and Miss Gurney, Lord and Lady Chesham, Lady Rossmore and Miss Naylor, Lord Kenyon, Lord Garioch, Lady Alice Portal, Lady Margaret Levett and the Ladies Ashley, Lady W. Nevill, Lord Paulet, Lady Charles Beresford, Lady Forbes and Misses Forbes, Lady Claud Hamilton, Lord Carlow, Lady Mary Mills, Lord Lurgan, Lord Henry Vane Tempest, Lord and Lady Algernon Gordon Lennox, Lord Richard Nevill, the Hon. W. Coventry, the Hon. G. Joliffe, the Hon. Schomberg M'Donnell, the Hon. H. Coventry, Captain the Hon. E. Dawson, the Hon. Alistair and Mrs. Hay, the Hon. Mrs. Grosvenor, [[Social Victorians/People/Bourke|the Hon. Algernon and Mrs. Bourke]], the Hon. F. Dawnay, the Hon. E. J. Mills, the Hon. A. Johnstone, the Hon. Claude Hay, the Hon. Sidney Greville, the Hon. Mr. Dundas and Lady Hilda Dundas, the Hon. Thomas and Lady Idina Brassey and the Hon. Muriel Brassey, the Hon. Mr. Mansfield, Colonel the Hon. Henry Byng and Miss Byng, the Hon. Mrs. Oliphant, the Hon. Mr. Harbord, the Right Hon. Henry Chaplin, M.P., the Hon. G. Somerset, Sir William Gordon Cumming, Sir George Arthur, Sir Hubert Miller, Sir Charles Forbes, Sir William and Lady Eden, Sir George Chetwynd, Sir Frederick Johnstone, Sir John D. Poynder, Colonel and Lady Emma Crichton, the Hon. Miss Harbord, Captain and Lady Jane Combe, Colonel Paget, Captain Williams, Captain Ford, Captain Doyle, Captain Hanbury, Captain Campbell, Captain Constable, Captain Kinloch, Captain Longfield, M. Gutmansthal, Mrs. Bingham, Mr. Guthrie, Mrs. Arthur Paget, Mrs. Charles Wilson and Miss Wilson, Mr. Hulse, M.P., and Mrs. Hulse, Mr. de Murrieta, Mrs. Bischoffsheim, Mr. Spencer Portal, Mr. and Mrs. Gerald Paget, Mr. Leigh and Miss Leigh, Mr. Percy Daniell, Mr. Lister, Mr. Frederick Vincent, Mr. Cazalet, Mr. Alfred de Rothschild, Mr. John Savile Lumley, Mr. and Mrs Leopold de Rothschild, Mr. and Mrs. Skeffington Smith and Miss Taylor, Mrs. George Cavendish Bentinck, Mr. Alfred Farquhar, [[Social Victorians/People/Fanny Ronalds|Mr. Reginald Ronalds]], Miss Alice Ellice, Mr. George Marjoribanks, Mr. Wyndham, Mr. Dugdale, Mr. Montagu, Mrs. Sneyd, Mr. Wynn, Mr. Edward Hamilton, Mr. Murray Guthrie, Mr. George Lambert, Mrs. Sanford, Miss Mabel Forbes. Mr. Herbert Magniac, Mr. Bailey, Mr. Milner, Mr. Charles Kindersley, Mr. Beaumont, Mr. Walter Hervey, Mr. H. Hoare, Mr. Foley, Mr. Scott Murray, Mr. Coventry, Mr. Bertie, Mr. Jarvis, Mr. Guthrie, Mr. George Cavendish Bentinck, Mr. E. Charteris, Mr. Cholmondeley, Mr. Oswald Magniac, Mr. Cecil Campbell, Mr. and Mrs. Henry Oppenheim, Mr. Peploe, Mr. A. Charteris, Mr. Seymour Gore, Mr. Robert Antrobus, Mr. Elliot, M. de Champs, Mr. Wombwell, Mr. Charles Hoare, M.P., and many others.&lt;ref&gt;&quot;Lord Alington's Ball.&quot; ''Morning Post'' 25 July 1890, Friday: 3 [of 8], Col. 5 b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18900725/014/0003. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

==August 1890==
===6 August 1890, Friday===

==== Beautiful Women ====
The ''Lancaster Observer and Morecambe Chronicle'' reprinted a story from ''Vanity Fair'' about &quot;Beautiful Women&quot;:&lt;blockquote&gt;Beautiful Women. — ''Vanity Fair'' asks what country in the world can show a more beautiful bevy of women than England? When Lady Helen Vincent, with her sister, Lady Cynthia Graham; when Lady Warwick with her sisters, the Duchess of Sutherland and Lady Westmorland; and when Lady Mar and Kellie, Lady de Trafford, Princess Pless, Lady de Gray[,] Lady Naylor-Leyland, the Duchess of Portland, Lady Alington, Lady Sophie Scott, Lady Chelsea, [[Social Victorians/People/Bourke|Lady Algernon Bourke]], Lady Henry Bentinck, Mrs. Willie Grenfell, Mrs. Rupert Beckett, Mrs. Arthur Paget, and Countess Clary are gathered together it is a sight to make an old man young; while Mrs. Gerard Leigh and her sister, Lady Yarborough, and Lady Powis, Lady Norreys, Mrs Farquharson, Mrs. Willie James, Lady Dalkeith, Mrs. Pretyman, Mrs. Gervase Beckett, Lady Rossmore, Lady Sarah Wilson, Lady Colebrook, Lady Hartopp, Mrs. Willie Walker, and Lady Milton are almost equally admired. The many pretty girls include Miss Enid and Miss Muriel Wilson, who still head the list of the unmarried beauties, Lady Beatrice Butler, Lady Alexandra Hamilton, Miss Kennard, Miss Madeline Bourke, and Miss Leila Crichton; while among the debutantes Lady Evelyn Crichton and Lady Vivian's daughters have had a great success, and Lady Alice Montagu, petite and charmingly pretty, has been so much admired. The daughters of Lady Gosford, Lady Verulam, Lady Leitrim, Lady Inchiquin, and Lady Grey have also been admired, as well as Lady Helen Stewart, Lady Katherine Scott, and Miss Chaplin.&lt;ref&gt;&quot;Beautiful Women.&quot; ''Lancaster Observer and Morecambe Chronicle'' 6 August 1897, Friday: 2 [of 8], Col. 5b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001804/18970806/023/0002. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

===25 August 1890, Monday===
Summer Bank Holiday

==September 1890==
==October 1890==
===22 October 1890, Wednesday===
Arnold Dolmetsch went to the Reading Room (Campbell 22).

===25 October 1890, Saturday===
[[Social Victorians/Loder De Vere Beauclerk Wedding|Loder—De Vere Beauclerk Wedding]]

===31 October 1890, Friday===
Halloween.

==November 1890==
===5 November 1890, Wednesday===
Guy Fawkes Day
===19 November 1890, Wednesday===
Arnold Dolmetsch, with some of his students and his daughter Helene, provided musical illustrations for a lecture given by Dr. Frederick Bridge on &quot;Mozart as Teacher,&quot; probably at Gresham College, where Bridges was professor (Campbell 34).

===21 November 1890, Friday===
Dr. Frederick Bridge's last fall 1890 lecture at Gresham College, for which Dolmetsch provided illustration. Campbell says, &quot;it is, in fact, the first record in modern times of music by Byrd, Dr. Bull, Jenkins, Simpson, Lawes, Locke and Purcell being played 'on the instruments for which it was written'&quot; (Campbell 34).

===25 November 1890, Tuesday===
Arnold Dolmetsch got a three-month pass to the Reading Room and &quot;thereafter held yearly tickets until 1916&quot; (Campbell 22).

==== 1890 November 29, Saturday ====

===== [[Social Victorians/Dudley-Beckwith Wedding 1890-11-29|Wedding of Francis Dudley, Lord Leigh and Héléne Forbes Beckwith]] =====

==December 1890==
Sometimes in December 1890, [[Social Victorians/People/William Robert Woodman|William Woodman]], one of the founding members of the [[Social Victorians/Golden Dawn|Golden Dawn]], died (Gilbert 86 12).

=== 4 December 1890, Thursday ===

==== [[Mure-Portal Wedding 1890-12-04|Wedding of Miss Mure and Mr. S. J. Portal]] ====

===19 December 1890, Friday===
&quot;The eleventh annual ''Truth'' Toy Exhibition for the children in London hospitals, workhouses, and infirmaries was held at the Grosvenor Gallery, Bond-street, on Dec. 19 and 20. There are over 22,000 children in these institutions, and each of them has a separate toy, besides the large and more expensive toys which are presented for the general use of the inmates. A special feature of the show was the dolls dressed by lady readers of ''Truth''. Several special donations in connection with the fund have been made, the principal of which is that of 10,200 new sixpences sent for distribution by the same liberal donor who has given a similar present on former occasions; while Mr. Tom Smith has had specially made, and has forwarded for distribution, over 22,000 crackers; and Mr. Horniman (as stated in our last issue) has given to the adults in hospitals and workhouses 1200 packets of tea, to be given to them as Christmas boxes.&quot; (Illustrated London News (London, England), Saturday, December 27, 1890; pg. 806; Issue 2697, Col. B)

===20 December 1890, Saturday===
&quot;In order that the adults connected with the hospitals and workhouses may participate in the good things given to the children in the ''Truth'' toy distribution, Mr. F. J. Horniman, of Wormwood-street, City, has sent Mr. Labouchere 1200 packets of tea to be given to them as a Christmas box.&quot; (Illustrated London News (London, England), Saturday, December 20, 1890; pg. 774; Issue 2696, Col. B) 

From the ''Times'', 22 December 1890, &quot;The Late Sir Edgar Boehm&quot;: &lt;blockquote&gt;On Saturday, in accordance with the special request of the Queen, the late Sir Edgar Boehm, R.A., was buried in St. Paul’s Cathedral, in the south aisle of the crypt, the spot being known as “The Painters Corner.” [new paragraph] The funeral cortége left the residence of the deceased at about 11 o’clock, there being five mourning and several private carriages. In the first carriage were the chief mourners, Sir Edgar Collins Boehm, the only son of the late baronet, and Mr. Conrad Herapath. The second and third carriages were occupied by Sir Frederic Leighton, P.R.A., Sir Nigel Kingscote, Mr. Richard Mills, Colonel Francis Baring, Mr. Alma-Tadema, R.A., Sir R. H. Collins, Mr. Edward J. Poynter, R.A., and Mr. Duncan MacGregor, all of whom subsequently, at the cathedral, acted as pall bearers. The fourth carriage contained representatives of the Council of the Royal Academy – Mr. Edwin Long, R.A., Mr. J. B. Burgess, R.A., Mr. F. Goodall, R.A., and Mr. Beavis. In the fifth carriage were the following members of the professional staff of the deceased – Mr. R. Glassby, Mr. E. Lantéri, Signor Finili, and Herr Gross. The cortége stopped for a few moments at the Royal Academy, in order that it might be joined by two carriages containing other representatives of the institution. Leaving Piccadilly, the route taken was Waterloo-place, Pall-mall, Cockspur-street, the Strand, Fleet-street, and Ludgate-hill, the cathedral being reached about noon.

The procession was met at the great west door by Canon Gregory, the Archdeacon of London, the Rev. Dr. Baker, Minor Canons Milman, Russell, and Kelly, and the choir, who had a few minutes previously left the vestry; by Major Bigge, Equerry to the Queen, representing her Majesty; Colonel Stanley Clarke, who attended on behalf of the Prince and Princess of Wales; and Colonel W. J. Colville, representing the Duke of Edinburgh. The [[Social Victorians/People/Princess Louise|Princess Louise]] (Marchioness of Lorne) attired in deep mourning, and accompanied by [[Social Victorians/People/Arthur Collins|Lieut.-Col. Arthur Collins]] and Lady Sophia Macnamara, arrived at the cathedral a few minutes before 12 o’clock, and was conducted to a seat in the south side of the nave, close to the late Sir Edgar Boehm’s two daughters, upon whom her Royal Highness had called earlier in the morning. As the procession came slowly up the nave towards the chancel, “I am the resurrection of life” and other sentences of the burial service were chanted to music by Dr. Croft. The coffin, which was completely hidden by splendid wreaths, was preceded by the choristers and the clergy. Then followed Sir E. C. Boehm, with Mr. Conrad Herapath and Mr. Alfred Gilbert, A.R.A., the officers and council of the Royal Academy, and members of the deceased’s studio. The coffin was deposited upon a bier, which had been placed under the dome in front of the opening into the crypt, through which the body was subsequently lowered. The mourners having been conducted to the seats which had been reserved for them, and the clergy and choir having proceeded to their places in the chancel, Psalms xxxix. and xc. Were sung to music by Purcell and Felton, followed by Spohr’s anthem, “Blest are the departed,” and the lesson 1 Cor. Xv. 20, which was read by Canon Gregory. Whilst the hymn “Days and moments quickly flying” was being sung the Archdeacon of London and Minor Canon Milman proceeded from the chancel and took up positions by the side of the coffin. The remainder of the service preceding and following the lowering of the body into the crypt was read by Minor Canon Milman, and the collect was impressively recited by Archdeacon Sinclair. The late Dr. Newman’s beautiful hymn, “Lead kindly light,” was afterwards sung by the choir, and the service was brought to a close by Beethoven’s Funeral March, which was played in compliance with the special request of her Majesty, at whose desire also Chopin’s Funeral March had preceded the service. Dr. Martin was the organist.

While Beethoven’s march was being played the son and daughters of the late “Sculptor in ordinary to her Majesty,” together with other mourners, descended the crypt by the door near Howard’s monument, and saw the coffin for the last time. It bore the following inscription:- “Joseph Edgar Boehm. Born July 6, 1834; died at his work December 12, 1890. Thy will be done.” The coffin had already been deposited in the brick grave prepared for it, which is next to that of Sir Edwin Landseer. Immediately around it lie the remains of painters and sculptors of bygone days – Sir Joshua Reynolds, James Barry, Benjamin West, Henry Fuseli, Sir Thomas Lawrence, J. M. W. Turner, and John Henry Foley, while within half-a-dozen yards is the tomb of the great architect of the cathedral, Sir Christopher Wren. The coffin as last seen was covered by the floral tributes of loving friends, the symbolic laurel wreath forwarded by her Majesty surmounting them. This bore the inscription, “A tribute of gratitude for many beautiful memorial works executed for her. From Victoria, R. I.” Attached to the beautiful wreath sent by the Prince and Princess of Wales were the words, “A token of sincere regard and friendship.” Wreaths were forwarded by other members of the Royal Family, by Sir John and Lady Millais, Lord and Lady Reay, the Countess Sydney, Lord and Lady de Vesci, Mr. Henry Irving, Mr. and Mrs. Bancroft, by members of the council, students and officers of the Royal Academy, the Society of Artistic Sculptors (Vienna), and by the London Hungarian Association.&quot; (http://glassby.com/Chapter1.htm) &lt;/blockquote&gt;

===24 December 1890, Wednesday===
&quot;The people of South London and adjacent suburbs have to be grateful to Mr. Frederick Horniman, a well-known City merchant residing at Dulwich, for a munificent and beneficial Christmas gift. This gentleman has, during thirty years, formed a collection, worth above £100,000, of specimens of art, European, Indian, Chinese, and Japanese, also of decorative manufactures, and of ethnology and natural history, and rare books and manuscripts, at Surrey House, Forest Hill, which he intends to present to the public. The museum was opened by Sir Morell Mackenzie on Wednesday afternoon, Dec. 24. It already comprises twenty-four rooms, containing many beautiful specimens of horse and chain armour, Elizabethan bed-room furniture, an old English parlour and pantry, an Oriental armoury, a bible and manuscript room, an Egyptian gallery, and ethnographical saloon, a book and embroidery saloon, a porcelain and glass room, and a zoological saloon, with two live Russian bears and a monkey. We may describe the museum further, after another visit. Our Artist has sketched, in the ethnograhical saloon, an idol's shrine, made of cocoanut-fibre, from Fiji. Mr. Horniman, in acknowledging a vote of thanks, said that in an adjoining house he had accumulated a vast library of bibles and entomological works and specimens. It was his intention to build a hall at the back of the present building to contain a thousand persons, while the galleries would contain a library, and a stage would be provided, so that both eye and ear could be amused. He also contemplated buying sufficient land to enable a public body to erect class-rooms and gymnasia. Three cheers were given for Mr. Horniman, and the company proceeded to inspect the museum.&quot; &quot;(Mr. F. Horniman's Museum, Forest Hill.&quot; Illustrated London News (London, England), Saturday, January 03, 1891; pg. 7; Issue 2698, Col. C)

===25 December 1890, Thursday===
Christmas Day
===26 December 1890, Friday===
Boxing Day
==Works Cited==
*&quot;Besant Chronology.pdf.&quot; From Anderson, Nancy Fix, Walter L Arnstein, Deborah Logan, and Susie L Steinbach, Volume Editors. Lives of Victorian Political Figures, Part III: Queen Victoria, Florence Nightingale, Annie Besant and Millicent Garrett Fawcett by their Contemporaries. Volume 3 of Lives of Victorian Political Figures. Series Editors, Nancy LoPatin-Lummis and Michael Partridge. London: Pickering and Chatto, 2008.
*Crawford, Elizabeth. The Women’s Suffrage Movement: A Reference Guide, 1866–1928. Google Books. Accessed 14 October 2010.</text>
      <sha1>e7exydul7xm74s8rvxd6l9cs0pcwwk5</sha1>
    </revision>
  </page>
  <page>
    <title>Solving simultaneous equations</title>
    <ns>0</ns>
    <id>266023</id>
    <revision>
      <id>2833755</id>
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      <timestamp>2026-09-18T11:04:48Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Solving 3 by 4 */</comment>
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      <text bytes="79408" sha1="gefi0spaydn17x0to6s0yhvjzpk26ec" xml:space="preserve">==Introduction==
The word &quot;simultaneous&quot; implies that two or more equations exist in the same context at the same time.

For example:

&lt;math&gt;3x + 2y - 13 = 0\ \dots\ (1)&lt;/math&gt;

&lt;math&gt;2x - y - 4 = 0 \ \dots\ (2)&lt;/math&gt;

Equations &lt;math&gt;(1)&lt;/math&gt; and &lt;math&gt;(2)&lt;/math&gt; are 2 simultaneous equations.

When we see two simultaneous equations, it's natural to ask the question: What are the values of &lt;math&gt;x&lt;/math&gt;
and &lt;math&gt;y&lt;/math&gt; that satisfy both equations &lt;math&gt;(1)&lt;/math&gt; and &lt;math&gt;(2)&lt;/math&gt;?

To calculate &lt;math&gt;(x,y)&lt;/math&gt; common to both &lt;math&gt;(1)&lt;/math&gt; and &lt;math&gt;(2)&lt;/math&gt;:

&lt;math&gt;(2)*2\ \dots\ 4x - 2y - 8 = 0 \ \dots\ (3)&lt;/math&gt;

&lt;math&gt;(3)+(1)\ \dots\ 7x - 21 = 0;\ x = 3.&lt;/math&gt;

Substitute &lt;math&gt;3&lt;/math&gt; for &lt;math&gt;x&lt;/math&gt; in &lt;math&gt;(2):\ 2(3) - y - 4 = 0;\ y = 2.&lt;/math&gt;

The values &lt;math&gt;(x,y)=(3,2)&lt;/math&gt; satisfy both equations &lt;math&gt;(1)&lt;/math&gt; and &lt;math&gt;(2).&lt;/math&gt;

In cartesian coordinate geometry of 2 dimensions, point &lt;math&gt;(3,2)&lt;/math&gt; is the point of intersection
of two lines &lt;math&gt;(1)&lt;/math&gt; and &lt;math&gt;(2).&lt;/math&gt; See Figure 1 below.

If the 2 lines are parallel, there is no point of intersection. See Figure 2 below.

The trivial solution &lt;math&gt;(0, 0)&lt;/math&gt; is a valid solution. See Figure 3 below.
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0726_2lines.png|&lt;small&gt;Figure 1. 2 lines that intersect at point (3,2).&lt;/small&gt;
File:0726_2parallelLines.png|&lt;small&gt;Figure 2. When 2 lines are parallel, there is no point of intersection.&lt;/small&gt;
File:0729_2lines.png|&lt;small&gt;Figure 3. The trivial solution x=y=0 is a valid solution.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}
The information contained in equations &lt;math&gt;(1)&lt;/math&gt; and &lt;math&gt;(2)&lt;/math&gt; may constitute a matrix:

&lt;pre&gt;
[
  [3,  2, -13],
  [2, -1,  -4]
]
&lt;/pre&gt;

In fact, in the python programming language, the following statement is valid code:

&lt;syntaxhighlight lang=python&gt;
data = [
  [3,  2, -13],
  [2, -1,  -4]
]
&lt;/syntaxhighlight&gt;

For there to be a point of intersection, &lt;code&gt;data&lt;/code&gt; must be valid.

Here are examples of invalid data:
&lt;syntaxhighlight lang=python&gt;
data = [
  [3,  2, -13],  # Both lines are parallel.
  [6,  4,  -5]   # See Figure 2 above.
]
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
data = [
  [3,  2, -13],
  [0,  0,  -4] # Empty row, representing equation 0x + 0y - 4 = 0.
]
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
data = [
  [3,  0, -13], # Empty column representing 2 parallel lines:
  [2,  0,  -4]  # 3x = 13 and 2x = 4.
]
&lt;/syntaxhighlight&gt;

The matrix above with name &quot;data&quot; is described as matrix &quot;2 by 3,&quot; meaning that it contains 2 rows with 3 columns or 3 members per row.
==Solving 2 by 3==
Below is python code containing function &lt;code&gt;solve2by3 (input).&lt;/code&gt; The function accepts as input a matrix like 
&lt;code&gt;data&lt;/code&gt; above.

After the code are examples of invocation with both good data and bad data.
&lt;syntaxhighlight lang=python&gt;
import sys

def solve2by3 (input) :
    '''
input represents system:
a1*x + b1*y + c1 = 0
a2*x + b2*y + c2 = 0

input = (
(a1,b1,c1),
(a2,b2,c2),
)

To invoke:
x,y = solve2by3 (input)
Function solve2by3 () may return None.

input is not changed by this function.
'''
    def solve2by3_(input) :
        row1,row2 = input
        a1,b1,c1 = row1
        a2,b2,c2 = row2

        if ( (a1 == b1 == 0) or (a2 == b2 == 0) ) :
            print ('solve2by3() : empty row in input.')
            return None
        if (a1 == a2 == 0) or (b1 == b2 == 0) :
            print ('solve2by3() : empty column in input.')
            return None
        if a1*b2 == a2*b1 :
            print ('solve2by3() : parallel input.')
            return None
        if c1 == c2 == 0 :
            # Column is empty. However, trivial solution is valid.
            return 0,0

# Arrange input, if necessary, to ensure that a1 is non-zero.
        if a1 : pass
        else :
            row1,row2 = row2,row1
            a1,b1,c1 = row1
            a2,b2,c2 = row2

# The matrix is:
# a1, b1, c1 with a1 non-zero.
# a2, b2, c2
# Process row2, if necessary,  so that a2 becomes 0.

        if a2 :
            if a2 == a1 :
                b2_,c2_ =  b1-b2, c1-c2
            else:
                L1 = [a2*v for v in row1]
                L2 = [a1*v for v in row2]
                zero,b2_,c2_ = [ L1[p]-L2[p] for p in (0,1,2) ]
                if zero :
                    # Theoretically this should not happen.
                    # It may happen if, for example, limited precision
                    # of floats causes small rounding errors.
                    print ('solve2by3() : Internal error 1.')
                    return None
        else : b2_,c2_ =  b2,c2

# The matrix is:
# a1, b1,  c1  with a1 non-zero
# 0,  b2_, c2_ and a2 zero.

        # 0*x + b2_*y + c2_ = 0
        # b2_*y = - c2_
        y = -c2_/b2_

        # a1*x + b1*y + c1 = 0
        # a1*x = -( b1*y + c1 )
        x = -(c1 + b1*y)/a1 # Here is why a1 must be non-zero.

        return x,y

# Following is python code used for trapping errors
# that may occur in function solve2by3_() above.
    output = error = ''
    try : output = solve2by3_(input)
    except : error = sys.exc_info()[:2]
    if (output == None) or error :
        if error :
            print ('solve2by3() :')
            print ('  error detected in processing.')
            print ('   ', error)
        print ('  input =')
        print ('   ', input[0])
        print ('   ', input[1])
        return None
    return output
&lt;/syntaxhighlight&gt;
Invocation with good data:
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve2by3([
  [3,  2, -13],
  [2, -1,  -4]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
(3.0, 2.0)
&lt;/pre&gt;
{{RoundBoxBottom}}
Invocation with bad or invalid data:
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve2by3([
  [3,  2, -13],  # Both lines are parallel.    
  [6,  4,  -5]   # See Figure 2 above.         
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : parallel input.
  input =
    [3, 2, -13]
    [6, 4, -5]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve2by3([
  [3,  2, -13, 7], # Input matrix not exactly 2 by 3.
  [6,  4,  -5]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() :
  error detected in processing.
    (&lt;class 'ValueError'&gt;, ValueError('too many values to unpack (expected 3)',))
  input =
    [3, 2, -13, 7]
    [6, 4, -5]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve2by3([
  [3,  0, 2],
  [6,  0, 4]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : empty column in input.
  input =
    [3, 0, 2]
    [6, 0, 4]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
===Reversing the process===
====Linear Function====
[[File:1212line01.png|thumb|400px|'''
Figure 1. Diagram of line defined by 2 points.'''
&lt;/br&gt;
2 points are: &lt;math&gt;(-5,4), (3,1).&lt;/math&gt;
&lt;/br&gt;
Equation of line is: &lt;math&gt;3x + 8y - 17 = 0.&lt;/math&gt;
]]
Examples above calculate the point of intersection of 2 lines. 

An example of reversing the process is this task:

Given two points &lt;math&gt;(x_1, y_1), (x_2, y_2)&lt;/math&gt; calculate equation of line containing these 2 points.

Equation of line is of format &lt;math&gt;Ax + By + C = 0,&lt;/math&gt;

For example: &lt;math&gt;3x + 2y + 10 = 0\ \dots\ (1).&lt;/math&gt;

Equation &lt;math&gt;(1)&lt;/math&gt; can be expressed as &lt;math&gt;6x + 4y + 20 = 0&lt;/math&gt; or &lt;math&gt;-9x - 6y - 30 = 0.&lt;/math&gt;

Also, there appear to be 3 unknowns, but only two sets of values are required to define the line.


Assume &lt;math&gt;C = 1&lt;/math&gt; and the 2 relevant equations are:

&lt;math&gt;Ax_1 + By_1 + 1 = 0&lt;/math&gt;

&lt;math&gt;Ax_2 + By_2 + 1 = 0&lt;/math&gt;


To solve for &lt;math&gt;A, B:&lt;/math&gt;

&lt;math&gt;x_1A + y_1B + 1 = 0&lt;/math&gt;

&lt;math&gt;x_2A + y_2B + 1 = 0&lt;/math&gt;

Suppose the line is defined by points &lt;math&gt;(3,1), (-5,4):&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:
input = [
    [3,1,1],
    [-5,4,1],
]
result = solve2by3 (input)
print (result)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(-0.17647058823529413, -0.47058823529411764)
&lt;/syntaxhighlight&gt;
Desired equation is: &lt;math&gt;-0.17647058823529413\cdot x -0.47058823529411764\cdot y + 1 = 0\ \dots\ (2).&lt;/math&gt;

To improve appearance of &lt;math&gt;(2):&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:

print (A/B)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
0.37500000000000006
&lt;/syntaxhighlight&gt;
Let &lt;math&gt;A, B = 3, 8&lt;/math&gt; and check:
&lt;syntaxhighlight lang=python&gt;
# python code

A,B = 3,8

p1 = x1,y1 = 3,1
p2 = x2,y2 = -5,4

for v in (p1,p2) :
    x,y = v
    C = -(A*x + B*y)
    s1 = 'C'
    print (s1, eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
C -17
C -17
&lt;/syntaxhighlight&gt;
Desired equation &lt;math&gt;(2)&lt;/math&gt; becomes &lt;math&gt;3x + 8y - 17 = 0\ \dots\ (3).&lt;/math&gt;

====Wrong assumptions====
[[File:1212line02.png|thumb|400px|'''
Figure 2. Diagram of line defined by 2 points and passing through origin.'''
&lt;/br&gt;
2 points are: &lt;math&gt;(3,2), (6,4).&lt;/math&gt;
&lt;/br&gt;
Equation of line is: &lt;math&gt;2x - 3y = 0.&lt;/math&gt;
&lt;/br&gt;
Non-zero value for coefficient &lt;math&gt;C&lt;/math&gt; is impossible.
]]
Sometimes you create a matrix that seems correct, but it fails to produce a result.
Here is such an example:

What is equation of line defined by points &lt;math&gt;(3, 2), (6, 4)?&lt;/math&gt;

As above assume that &lt;math&gt;C = 1.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:

p1 = x1,y1 = 3,2 
p2 = x2,y2 = 6,4
input = [
    [x1,y1,1],
    [x2,y2,1],
]

result = solve2by3 (input)
print (result)
&lt;/syntaxhighlight&gt;
This assumption failed:
&lt;syntaxhighlight&gt;
solve2by3() : parallel input.
  input =
    [3, 2, 1]
    [6, 4, 1]
None
&lt;/syntaxhighlight&gt;
Assume that &lt;math&gt;A = 1.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:

# 1(x1) + B(y1) + 1(C) = 0
# 1(x2) + B(y2) + 1(c) = 0

# y1(B) + 1(C) + x1 = 0
# y2(B) + 1(C) + x2 = 0

input = [
    [y1,1,x1], # Notice that input has been
    [y2,1,x2], # rotated left by one column.
]

result = solve2by3 (input)
print (result)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(-1.5, 0.0)
&lt;/syntaxhighlight&gt;
Equation of line is: &lt;math&gt;1\cdot x + (-1.5)\cdot y + 0 = 0&lt;/math&gt; or &lt;math&gt;2x - 3y = 0&lt;/math&gt;

This line includes the origin. Therefore constant &lt;math&gt;C&lt;/math&gt; cannot be non-zero.


Generally:

* Without rotation, &lt;math&gt;A, B = \text{result}&lt;/math&gt; and &lt;math&gt;C = 1.&lt;/math&gt;

* With rotation left by one column, &lt;math&gt;B, C = \text{result}&lt;/math&gt; and &lt;math&gt;A = 1.&lt;/math&gt; 


In this case:
&lt;syntaxhighlight lang=python&gt;
# python code:
&gt;&gt;&gt; B,C = result ; A = 1
&gt;&gt;&gt; A,B,C
&gt;&gt;&gt; 1,-1.5,0
&lt;/syntaxhighlight&gt;


For example of big matrix that failed the first time, but was successful the second time, see
[https://en.wikiversity.org/wiki/Solving_simultaneous_equations#Cubic_Resistive_Network cubic resistive network]
below.

==Solving 3 by 4==
Below is python code containing function &lt;code&gt;solve3by4 (input).&lt;/code&gt; The function accepts as input a 3 by 4 matrix like 
that described in the code comments.

In 3d coordinate geometry the equations &lt;code&gt;(1), (2), (3)&lt;/code&gt; are the equations of 3 planes and the solution of the system
is the point of intersection of the 3 planes.

Given 3 random planes, there are 2 conditions that do not produce a unique point of intersection:

* If 2 of the planes are parallel. See Figure 1 below.

* If the 3 planes form a &quot;tent&quot; or &quot;delta.&quot; See Figure 2, 3 or 4 below. A special case of this condition occurs when size of &quot;tent&quot; is zero, in which case all three planes intersect on a common line and there is an infinite number of solutions. See Figure 5 below.
The trivial solution &lt;math&gt;(0, 0, 0)&lt;/math&gt; is valid. See Figure 6 below.
&lt;code&gt;&lt;/code&gt;
&lt;code&gt;&lt;/code&gt;
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0726_2parallelPlanes.png|&lt;small&gt;Figure 1. When 2 planes are parallel, there is no point of intersection.&lt;/small&gt;
File:0730triangularTube.png|&lt;small&gt;Figure 2. Triangular tube, 3 planes that never intersect.&lt;/small&gt;
File:0726_3planes0.png|&lt;small&gt;Figure 3. 3 planes that form a &quot;tent,&quot; view 1. There is no point of intersection.&lt;/small&gt;
File:0726_3planes1.png|&lt;small&gt;Figure 4. 3 planes that form a &quot;tent,&quot; view 2. There is no point of intersection.&lt;/small&gt;
File:1109_3planes1.png|&lt;small&gt;Figure 5. 3 planes that intersect on a common line. Points &lt;math&gt;(6,6,1),&lt;/math&gt; &lt;math&gt;(7,7,4),&lt;/math&gt; &lt;math&gt;(8,8,7)&lt;/math&gt; are on this line and are common to all 3 planes.&lt;/small&gt;
File:0729_3planes.png|&lt;small&gt;Figure 6. 3 planes that intersect at origin (0, 0, 0).&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}

&lt;syntaxhighlight lang=python&gt;
def solve3by4 (input) :
    '''
input represents system:
a1*x + b1*y + c1*z + d1 = 0 ... (1)
a2*x + b2*y + c2*z + d2 = 0 ... (2)
a3*x + b3*y + c3*z + d3 = 0 ... (3)

input = (
(a1,b1,c1,d1),
(a2,b2,c2,d2),
(a3,b3,c3,d3),
)

To invoke:
x,y,z = solve3by4 (input)
Function solve3by4 () may return None.

input is not changed by this function.
'''
    def checkDirectionNumbers (input) :
        row1,row2,row3 = input
        a1,b1,c1,d1 = row1
        a2,b2,c2,d2 = row2
        a3,b3,c3,d3 = row3
# The direction numbers of the lines of intersection.
        dn1 = [b3*c2-b2*c3, a2*c3-a3*c2, b2*a3-b3*a2]
        if dn1[0] == dn1[1] == dn1[2] == 0 :
            print ('checkDirectionNumbers() : 2 rows parallel, 2 and 3.')
            return
        dn2 = [b3*c1-b1*c3, a1*c3-a3*c1, b1*a3-b3*a1]
        if dn2[0] == dn2[1] == dn2[2] == 0 :
            print ('checkDirectionNumbers() : 2 rows parallel, 1 and 3.')
            return
        dn3 = [b1*c2-b2*c1, a2*c1-a1*c2, b2*a1-b1*a2]
        if dn3[0] == dn3[1] == dn3[2] == 0 :
            print ('checkDirectionNumbers() : 2 rows parallel, 1 and 2.')
            return
# Are 2 lines of intersection parallel?
# If so, and no 2 planes are parallel, the 3 planes form a tent.
        a2,b2,c2 = dn2
        a3,b3,c3 = dn3
        dn1 = [b3*c2-b2*c3, a2*c3-a3*c2, b2*a3-b3*a2]
        if dn1[0] == dn1[1] == dn1[2] == 0 :
            print ('checkDirectionNumbers() : 3 rows form a tent.');
            return

    def solve3by4_(input) :
        row1,row2,row3 = input
        a1,b1,c1,d1 = row1
        a2,b2,c2,d2 = row2
        a3,b3,c3,d3 = row3

        if (a1 == b1 == c1 == 0) or (a2 == b2 == c2 == 0) or (a3 == b3 == c3 == 0) :
            print ('solve3by4() : empty row in input.')
            return None
        if (a1 == a2 == a3 == 0) or (b1 == b2 == b3 == 0) or (c1 == c2 == c3 == 0) :
            print ('solve3by4(). empty column in input.')
            return None
        if (d1 == d2 == d3 == 0) :
            # This empty column means that trivial solution is valid.
            return 0,0,0

# Sort input if necessary so that a1 is non-zero.
        if a1 : pass
        elif a2 :
            row1,row2 = row2,row1
            a1,b1,c1,d1 = row1
            a2,b2,c2,d2 = row2
        else :
            row1,row3 = row3,row1
            a1,b1,c1,d1 = row1
            a3,b3,c3,d3 = row3

# The matrix is:
# a1, b1, c1, d1 with a1 non-zero.
# a2, b2, c2, d2
# a3, b3, c3, d3

# Process rows, if necessary, so that a2,a3 become zero.

        if a2 :
            L1 = [a2*v for v in row1]
            L2 = [a1*v for v in row2]
            zero,b2_,c2_,d2_ = [ L1[p]-L2[p] for p in (0,1,2,3) ]
        else : zero,b2_,c2_,d2_ =  a2,b2,c2,d2

        if a3 :
            L1 = [a3*v for v in row1]
            L2 = [a1*v for v in row3]
            zero,b3_,c3_,d3_ = [ L1[p]-L2[p] for p in (0,1,2,3) ]
        else : zero,b3_,c3_,d3_ =  a3,b3,c3,d3

# The matrix is:
# a1, b1,  c1,  d1 with a1 non-zero.
# 0,  b2_, c2_, d2_
# 0,  b3_, c3_, d3_
        data1 = (
(b2_, c2_, d2_),
(b3_, c3_, d3_),
)
        data2 = solve2by3(data1)
        if data2 == None :
            checkDirectionNumbers (input) # If solve2by3() fails, this line shows why.
            return None
        y,z = data2
        # a1*x + b1*y + c1*z + d1 = 0
        # a1*x = -( b1*y + c1*z + d1 )
        x = -(b1*y + c1*z + d1)/a1 # Here is why a1 must be non-zero.

        return x,y,z

    output = error = ''
    try : output = solve3by4_(input)
    except : error = sys.exc_info()[:2]

    if (output == None) or error :
        if error :
            print ('solve3by4() :')
            print ('  error detected in processing.')
            print ('   ', error)
        print ('  input of solve3by4() =')
        print ('   ', input[0])
        print ('   ', input[1])
        print ('   ', input[2])
        return None
    return output
&lt;/syntaxhighlight&gt;

Below are examples of invocation with both good data and bad data.

Invocation with good data:
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve3by4([
  [2,  -1, 3, -17],
  [1,  3, 2, -25] ,
  [3,  2, -1, -12] ,
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
(3.0, 4.0, 5.0)
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve3by4([
  [12,  -12, -5, -24],
  [-6,   15,  8,  12] ,
  [ 0,   10,  3,   0] ,
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
(2.0, 0.0, -0.0)
&lt;/pre&gt;
{{RoundBoxBottom}}
Invocation with bad or invalid data:
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve3by4([
    [20, 16, 2, 17],
    [-77, -27, -25, -24],
    [81, 45, 18, 43]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : parallel input.
  input =
    (-692, 346, -829)
    (396, -198, 517)
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    [20, 16, 2, 17]
    [-77, -27, -25, -24]
    [81, 45, 18, 43]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve3by4([
    [-34, -6, 34, -32],
    [82, 14, -82, 72],
    [-59, -45, 59, -88]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : empty column in input.
  input =
    (-16, 0, -176)
    (-1176, 0, -1104)
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    [-34, -6, 34, -32]
    [82, 14, -82, 72]
    [-59, -45, 59, -88]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve3by4([
    [34, -5, -21, 30],
    [-54, -33, 63, 62],
    [18, 11, -21, 38]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : parallel input.
  input =
    (1392, -1008, -3728)
    (-464, 336, -752)
checkDirectionNumbers() : 2 rows parallel, 2 and 3.
  input of solve3by4() =
    [34, -5, -21, 30]
    [-54, -33, 63, 62]
    [18, 11, -21, 38]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solve3by4([
    [20, 16, 2, 17],
    [-77, -27, '-25', -24],
    [81, 45, 18, 43]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve3by4() :
  error detected in processing.
    (&lt;class 'TypeError'&gt;, TypeError(&quot;unsupported operand type(s) for -: 'int' and 'str'&quot;,))
  input of solve3by4() =
    [20, 16, 2, 17]
    [-77, -27, '-25', -24]
    [81, 45, 18, 43]
None
&lt;/pre&gt;
{{RoundBoxBottom}}

===Reversing the Process===
====Quadratic function====
[[File:1212quadratic01.png|thumb|400px|'''
Figure 1. Graph of quadratic function defined by 3 points.'''
]]
A quadratic function &lt;math&gt;y = f(x) = Ax^2 + Bx + C&lt;/math&gt; is defined by 3 points:
&lt;math&gt;(-2, 9.0), (5, 4.8), (10, 13.8).&lt;/math&gt;


What is &lt;math&gt;f(x)?&lt;/math&gt;


&lt;math&gt;y = Ax^2 + Bx + C&lt;/math&gt;

&lt;math&gt;A, B, C&lt;/math&gt; are 3 unknowns.

&lt;math&gt;x^2(A) + x(B) + 1(C) - y = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:

x1,y1 = -2, 9
x2,y2 =  5, 4.8
x3,y3 = 10, 13.8

input = [
    [x1**2, x1, 1, -y1],
    [x2**2, x2, 1, -y2],
    [x3**2, x3, 1, -y3],
]

A, B, C = solve3by4 (input)
s1 = 'A,B,C'
print (s1, eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
A,B,C (0.2, -1.2, 5.8)
&lt;/syntaxhighlight&gt;
&lt;math&gt;y = f(x) = 0.2x^2 - 1.2x + 5.8&lt;/math&gt;

====Wrong assumptions====
[[File:1212plane02.png|thumb|400px|'''
Figure 2. Graph of plane containing X axis.'''
&lt;/br&gt;
Because plane passes through origin, non-zero value for coefficient &lt;math&gt;D&lt;/math&gt; is impossible.
&lt;/br&gt;
Because plane is parallel to &lt;math&gt;X&lt;/math&gt; axis, non-zero value for coefficient &lt;math&gt;A&lt;/math&gt; is impossible.
]]
In 3 dimensions a plane (&lt;math&gt;Ax + By + Cz + D = 0&lt;/math&gt;) is defined by 3 points:
&lt;math&gt;(5, 3, -2), (-1, 12, -8), (37, 15, -10).&lt;/math&gt;

What is equation of plane?


&lt;math&gt;Ax + By + Cz + D = 0&lt;/math&gt;

&lt;math&gt;xA + yB + zC + D = 0&lt;/math&gt;

Assume that 
&lt;math&gt;D = 1.&lt;/math&gt;

&lt;math&gt;xA + yB + zC + 1 = 0&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

pt1 = x1,y1,z1 = (5, 3, -2)
pt2 = x2,y2,z2 = (-1, 12, -8)
pt3 = x3,y3,z3 = (37, 15, -10)

input = [
    [ 5,  3,  -2, 1],
    [-1, 12,  -8, 1],
    [37, 15, -10, 1],
]

result = solve3by4 (input)
s1 = 'result'
print (s1, eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
solve2by3() : parallel input.
  input =
    (-63, 42, -6)
    (36, -24, 32)
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    (5, 3, -2, 1)
    (-1, 12, -8, 1)
    (37, 15, -10, 1)
result None
&lt;/syntaxhighlight&gt;
Input was invalid. Rotate input left and try again.
&lt;syntaxhighlight lang=python&gt;
# python code.

input = [
    [ 3,  -2, 1,  5],
    [12,  -8, 1, -1],
    [15, -10, 1, 37],
]

result = solve3by4 (input)
s1 = 'result'
print (s1, eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
solve2by3() : empty column in input.
  input =
    (0, 9, 63)
    (0, 12, -36)
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    (3, -2, 1, 5)
    (12, -8, 1, -1)
    (15, -10, 1, 37)
result None
&lt;/syntaxhighlight&gt;
Input was invalid. Rotate input left and try again.
&lt;syntaxhighlight lang=python&gt;
input = [
    [ -2, 1,  5,  3],
    [ -8, 1, -1, 12],
    [-10, 1, 37, 15],
]

result = solve3by4 (input)
s1 = 'result'
print (s1, eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
result (1.5, 0, 0)
&lt;/syntaxhighlight&gt;
Without rotation: &lt;math&gt;A, B, C = \text{result}&lt;/math&gt; and &lt;math&gt;D = 1.&lt;/math&gt;

With rotation left: &lt;math&gt;B, C, D = \text{result}&lt;/math&gt; and &lt;math&gt;A = 1.&lt;/math&gt;

With another rotation left: &lt;math&gt;C, D, A = \text{result}&lt;/math&gt; and &lt;math&gt;B = 1.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:
C, D, A = (1.5, 0, 0) ; B = 1
A, B, C, D
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(0, 1, 1.5, 0)
&lt;/syntaxhighlight&gt;
Equation of plane is: &lt;math&gt;0x + 1y + 1.5z + 0 = 0&lt;/math&gt; or 
&lt;math&gt;2y + 3z = 0&lt;/math&gt;
=====A better method=====
{{RoundBoxTop|theme=3}}
There are four unknown values: &lt;math&gt;A,B,C,D.&lt;/math&gt;

Create matrix 4 by 5:
&lt;syntaxhighlight lang=python&gt;
# python code.

pt1 = x1,y1,z1 = (5, 3, -2)
pt2 = x2,y2,z2 = (-1, 12, -8)
pt3 = x3,y3,z3 = (37, 15, -10)

input = []

for (x_,y_,z_) in (pt1,pt2,pt3) :
    x,y,z = [ dD(v) for v in (x_,y_,z_) ]
    input += [ [ x,y,z,1,0 ] ]

# For valid plane at least one of A,B,C must be non-zero.
# For last condition let A + B + C = 5.
input += [ [ 1,1,1,0,-5 ] ]

A,B,C,D = solveMbyN(input)

print (input)
print ( '({})x + ({})y + ({})z + ({}) = 0'.format(A,B,C,D) )
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
[[ 5,  3,  -2, 1,  0], #  5A +  3B -  2C + 1D + 0 = 0
 [-1, 12,  -8, 1,  0], # -1A + 12B -  8C + 1D + 0 = 0
 [37, 15, -10, 1,  0], # 37A + 15B - 10C + 1D + 0 = 0
 [ 1,  1,   1, 0, -5]] #  1A +  1B +  1C + 0D - 5 = 0
 
(0)x + (2)y + (3)z + (0) = 0
&lt;/syntaxhighlight&gt;
Equation of plane is: &lt;math&gt;2y + 3z = 0.&lt;/math&gt;
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==Solving M by (M+1)==
Below is python code containing function &lt;code&gt;solveMbyN (input).&lt;/code&gt; The function accepts as input
a 4 by 5 matrix (or greater) like that described in the code comments.

This function is recursive, calling itself with M being reduced by 1 with each recursive invocation until the matrix is size 3 by 4 in which case function solve3by4() is called.

&lt;syntaxhighlight lang=python&gt;
# python code

import decimal
Decimal = decimal.Decimal
getcontext = decimal.getcontext

def reduceRow (row) :
    '''
This function calculates the max(abs) of all values in row,
divides all values by the max(abs) and returns the result.
[27, -15, 42] becomes [27/42, -15/42, 42/42].
Very small values are converted to zero.

To invoke:
output = reduceRow (row)
output is list or None
'''
    if False in [ isinstance(v,Decimal) for v in row ] :
        print ('reduceRow: non Decimal in input.', { type(v) for v in row })
        return None
    max = sorted([ abs(v) for v in row ])[-1]
    row = [ v/max for v in row ]
    almostZero = Decimal('1e-' + str( getcontext().prec ))
    row = [ (v, Decimal(0))[abs(v) &lt; almostZero] for v in row ]
    return row

enable_reduceRow = 0

def solveMbyN (input) :
    '''
input represents system:
a0*w + b0*x + c0*y + d0*z + e0 = 0
a1*w + b1*x + c1*y + d1*z + e1 = 0
a2*w + b2*x + c2*y + d2*z + e2 = 0
a3*w + b3*x + c3*y + d3*z + e3 = 0
or greater.
This solves a matrix of M rows by N columns where N = M+1 and M &gt;= 2

input = [
(a0,b0,c0,d0,e0),
(a1,b1,c1,d1,e1),
(a2,b2,c2,d2,e2),
(a3,b3,c3,d3,e3),
]

To invoke:
w,x,y,z = solveMbyN (input)
Function solveMbyN () may return None.

If input is size 15 by 16:
v1,v2,v3, .... ,v14,v15 = solveMbyN (input)

input is not changed by this function.
'''
    def solveMbyN_(input) :
        input = [ list(v) for v in input ]
        # input is now local, hard copy of original input.
        # This ensures that original input is not changed by this function.

        numberOfRows = len(input)
        numberOfColumns = numberOfRows+1

        if numberOfRows &lt; 2 :
            print ('solveMbyN()! len(input) &lt; 2.')
            return None
        if numberOfRows == 2 : return solve2by3(input)
        if numberOfRows == 3 : return solve3by4(input)

        for row in range (0, numberOfRows) :
            if len(input[row]) != numberOfColumns :
                print ('solveMbyN()! row with bad length.')
                print ('    row number',row,'of',numberOfRows,'rows has length',len(input[row]),'.')
                return None
            if True not in [ bool(v) for v in input[row][:-1] ] :
                print ('solveMbyN()! empty row in input, row number',row,'of',numberOfRows,'rows.')
                return None

        for column in range (0, numberOfRows) :
            sum = 0
            for row in range (0, numberOfRows) :
                sum = bool(input[row][column])
                if sum : break
            if not sum :
                print ('solveMbyN()! empty column in input. column number',column,'of',numberOfRows,'columns.')
                return None

        for column in (numberOfRows,) :
            sum = 0
            for row in range (0, numberOfRows) :
                sum = bool(input[row][column])
                if sum : break
            if not sum :
                # Empty column. Trivial solution is valid.
                return (0,) * numberOfRows

        if enable_reduceRow :
            # For matrices greater than 10 by 11 enable this piece of code.
            for row in range (0, numberOfRows) :
                data = reduceRow (input[row])
                if isinstance(data,list) :
                    input[row] = data

# Arrange input if necessary so that a0 is non-zero.
        if not input[0][0] :
            for p in range (1, numberOfRows) :
                if input[p][0] :
                    input[p], input[0] = input[0], input[p]
                    break
# The matrix is:
# [a0,b0,c0,d0,e0], with a0 non-zero,
# [a1,b1,c1,d1,e1],
# [a2,b2,c2,d2,e2],
# [a3,b3,c3,d3,e3],

# Process rows so that a1, a2, a3, .... become zero.
        a0 = input[0][0]
        for p in range (1, numberOfRows) :
            ap = input[p][0]
            if ap :
                L0 = [ input[0][q]*ap for q in range (0, numberOfColumns) ]
                Lp = [ input[p][q]*a0 for q in range (0, numberOfColumns) ]
                L_ = [ L0[q]-Lp[q] for q in range (0, numberOfColumns) ]
                if L_[0] :
                    # This should not happen.
                    print ('solveMbyN()! internal error 1.')
                    return None
                input[p] = L_

# The matrix is:
# [a0, b0, c0, d0, e0], with a0 non-zero,
# [ 0,b1_,c1_,d1_,e1_],
# [ 0,b2_,c2_,d2_,e2_],
# [ 0,b3_,c3_,d3_,e3_],
        data1 = [ input[p][1:] for p in range (1, numberOfRows) ]
# data1 = [
# [b1_,c1_,d1_,e1_],
# [b2_,c2_,d2_,e2_],
# [b3_,c3_,d3_,e3_] ]

        data2 = solveMbyN(data1) # Here is where function solveMbyN() calls itself.
        if data2 == None : return None
        topRow = input[0][1:]
# b0, c0, d0, e0 topRow
#  x,  y,  z     data2
        listOfProducts = [ topRow[p]*data2[p] for p in range (0, len(data2)) ] + topRow[-1:]
# listOfProducts = [ b0*x, c0*y, d0*z, e0 ]
        sumOfProducts = [ sum for sum in (0,) for p in listOfProducts for sum in (sum+p,) ][-1]
# sumOfProducts = [ b0*x, b0*x+c0*y, b0*x+c0*y+d0*z, b0*x+c0*y+d0*z+e0 ][-1]
# sumOfProducts =  b0*x + c0*y + d0*z + e0
#           a0*w + b0*x + c0*y + d0*z + e0 = 0
#           a0*w + sumOfProducts = 0

        w = -sumOfProducts/a0 # Here is why a0 must be non-zero.

        return (w,) + data2

    output = error = ''
    try : output = solveMbyN_(input)
    except : error = sys.exc_info()[:2]
    if (output == None) or error :
        if error :
            print ('solveMbyN()!')
            print ('  error detected in processing.')
            print ('   ', error)
        if len(input) &gt;= 4 :
            print ('  input of solveMbyN() with',len(input),'rows =')
            for row in input : print ('   ', row)
        return None
    return output
&lt;/syntaxhighlight&gt;

Below are examples of invocation with both good data and bad data.

Invocation with good data:
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&lt;syntaxhighlight lang=python&gt;
L1 = [
[Decimal('-870442133162'), Decimal('239132906684'), Decimal('397660499756'), Decimal('788825405004'), Decimal('156830886652'), Decimal('-87096140169')], 
[Decimal('-112130420352'), Decimal('-93605595828'), Decimal('-185262083472'), Decimal('-93369903383'), Decimal('-497973505065'), Decimal('-766710012513')], 
[Decimal('-142983492168'), Decimal('619713461197'), Decimal('-608752759383'), Decimal('-448477443042'), Decimal('-281161661751'), Decimal('-799463977245')], 
[Decimal('572854919541'), Decimal('-148673693908'), Decimal('341291756040'), Decimal('362403188059'), Decimal('-202136092949'), Decimal('-429932229578')], 
[Decimal('157632861972'), Decimal('330790263276'), Decimal('-836474627955'), Decimal('644295395386'), Decimal('-595590967129'), Decimal('-392835045727')]
]
output = solveMbyN(L1)
print (output)
&lt;/syntaxhighlight&gt;
The following results were produced with decimal precision set at 50:
&lt;pre&gt;
(
Decimal('-0.06331410760212760088313271882866553044211194694576'), Decimal('1.0969089506763419155148060427588009931309074487534'), Decimal('1.0837038580207682607126722016017867670831200359767'), Decimal('-0.42989566124678842791674322699930461340596671792215'), Decimal('-2.0541601084281682582146753421426610779297051535362')
)
&lt;/pre&gt;
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Invocation with bad or invalid data:
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solveMbyN([
    [-4, -6, 3, -4, -8, -8],
    [1, 0, 2, 5, 1, 7],
    [9, -3, -8, 4, 7, -5],
    [1, -9, 5, -2, 5, -2],
    [1, -3, -6, -3, -6, 6]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
# With each step towards solve2by3() the length of each number in digits can theoretically double.
solve2by3() : parallel input.
  input =
    (-181440, 181440, -101088)
    (90720, -90720, 406944)
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    [-756, -1176, 0, -1872]
    [-324, -744, 240, -936]
    [-324, -384, -120, -264]
  input of solveMbyN() with 4 rows =
    [-6, 11, 16, -4, 20]
    [-66, -5, -20, -44, -92]
    [-42, 23, -12, 12, -16]
    [-18, -21, -16, -32, 16]
  input of solveMbyN() with 5 rows =
    [-4, -6, 3, -4, -8, -8]
    [1, 0, 2, 5, 1, 7]
    [9, -3, -8, 4, 7, -5]
    [1, -9, 5, -2, 5, -2]
    [1, -3, -6, -3, -6, 6]
None
&lt;/pre&gt;
Provided that numbers are small, integers, floats and Decimal objects produce the same results:
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solveMbyN([
[-4.0, -6.0, 3.0, -4.0, -8.0, -8.0],
[1.0, 0.0, 2.0, 5.0, 1.0, 7.0],
[9.0, -3.0, -8.0, 4.0, 7.0, -5.0],
[1.0, -9.0, 5.0, -2.0, 5.0, -2.0],
[1.0, -3.0, -6.0, -3.0, -6.0, 6.0]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : parallel input.
  input =
    (-181440.0, 181440.0, -101088.0)
    (90720.0, -90720.0, 406944.0)
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    [-756.0, -1176.0, 0.0, -1872.0]
    [-324.0, -744.0, 240.0, -936.0]
    [-324.0, -384.0, -120.0, -264.0]
  input of solveMbyN() with 4 rows =
    [-6.0, 11.0, 16.0, -4.0, 20.0]
    [-66.0, -5.0, -20.0, -44.0, -92.0]
    [-42.0, 23.0, -12.0, 12.0, -16.0]
    [-18.0, -21.0, -16.0, -32.0, 16.0]
  input of solveMbyN() with 5 rows =
    [-4.0, -6.0, 3.0, -4.0, -8.0, -8.0]
    [1.0, 0.0, 2.0, 5.0, 1.0, 7.0]
    [9.0, -3.0, -8.0, 4.0, 7.0, -5.0]
    [1.0, -9.0, 5.0, -2.0, 5.0, -2.0]
    [1.0, -3.0, -6.0, -3.0, -6.0, 6.0]
None
&lt;/pre&gt;
{{RoundBoxBottom}}
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
output = solveMbyN([
[Decimal('-4'), Decimal('-6'), Decimal('3'), Decimal('-4'), Decimal('-8'), Decimal('-8')],
[Decimal('1'), Decimal('0'), Decimal('2'), Decimal('5'), Decimal('1'), Decimal('7')],
[Decimal('9'), Decimal('-3'), Decimal('-8'), Decimal('4'), Decimal('7'), Decimal('-5')],
[Decimal('1'), Decimal('-9'), Decimal('5'), Decimal('-2'), Decimal('5'), Decimal('-2')],
[Decimal('1'), Decimal('-3'), Decimal('-6'), Decimal('-3'), Decimal('-6'), Decimal('6')]
])
print (output)
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
solve2by3() : parallel input.
  input =
    (Decimal('-181440'), Decimal('181440'), Decimal('-101088'))
    (Decimal('90720'), Decimal('-90720'), Decimal('406944'))
checkDirectionNumbers() : 3 rows form a tent.
  input of solve3by4() =
    [Decimal('-756'), Decimal('-1176'), Decimal('0'), Decimal('-1872')]
    [Decimal('-324'), Decimal('-744'), Decimal('240'), Decimal('-936')]
    [Decimal('-324'), Decimal('-384'), Decimal('-120'), Decimal('-264')]
  input of solveMbyN() with 4 rows =
    [Decimal('-6'), Decimal('11'), Decimal('16'), Decimal('-4'), Decimal('20')]
    [Decimal('-66'), Decimal('-5'), Decimal('-20'), Decimal('-44'), Decimal('-92')]
    [Decimal('-42'), Decimal('23'), Decimal('-12'), Decimal('12'), Decimal('-16')]
    [Decimal('-18'), Decimal('-21'), Decimal('-16'), Decimal('-32'), Decimal('16')]
  input of solveMbyN() with 5 rows =
    [Decimal('-4'), Decimal('-6'), Decimal('3'), Decimal('-4'), Decimal('-8'), Decimal('-8')]
    [Decimal('1'), Decimal('0'), Decimal('2'), Decimal('5'), Decimal('1'), Decimal('7')]
    [Decimal('9'), Decimal('-3'), Decimal('-8'), Decimal('4'), Decimal('7'), Decimal('-5')]
    [Decimal('1'), Decimal('-9'), Decimal('5'), Decimal('-2'), Decimal('5'), Decimal('-2')]
    [Decimal('1'), Decimal('-3'), Decimal('-6'), Decimal('-3'), Decimal('-6'), Decimal('6')]
None
&lt;/pre&gt;
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{{RoundBoxBottom}}

===Sphere===
In cartesian coordinate geometry of three dimensions a sphere is represented by equation:

&lt;math&gt;x^2 + y^2 + z^2 + Ax + By + Cz + D = 0.&lt;/math&gt;

On the surface of a certain sphere there are 4 known points:

&lt;syntaxhighlight lang=python&gt;
# python code

point1 = (13,7,20)
point2 = (13,7,4)
point3 = (13,-17,4)
point4 = (16,4,4)
&lt;/syntaxhighlight&gt;

What is equation of sphere?

Rearrange equation of sphere to prepare for creation of input matrix:

&lt;math&gt;(x)A + (y)B + (z)C + (1)D + (x^2 + y^2 + z^2) = 0.&lt;/math&gt;

Create input matrix of size 4 by 5:

&lt;syntaxhighlight lang=python&gt;
# python code

input = []
for (x,y,z) in (point1, point2, point3, point4) :
    input += [ ( x, y, z, 1, (x**2 + y**2 + z**2) ) ]

print (input)
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
[ (13,   7, 20, 1, 618),
  (13,   7,  4, 1, 234),
  (13, -17,  4, 1, 474),
  (16,   4,  4, 1, 288), ] # Matrix containing 4 rows with 5 members per row.
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

result = solveMbyN(input)
print (result)
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
(-8.0, 10.0, -24.0, -104.0)
&lt;/syntaxhighlight&gt;

Equation of sphere is :

&lt;math&gt;x^2 + y^2 + z^2 - 8x + 10y - 24z - 104 = 0&lt;/math&gt;

===Quintic function===
[[File:1212quintic01.png|thumb|400px|'''
Figure 4. Graph of quintic function defined by 6 points.'''
]]
A quintic function &lt;math&gt;y = f(x) = Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex + F&lt;/math&gt; is defined by 6 points:
&lt;math&gt;(-8, 0), (-6, 0), (-3, 0), (1,0), (3,0), (5,10).&lt;/math&gt;


What is &lt;math&gt;f(x)?&lt;/math&gt;


&lt;math&gt;y = f(x) = Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex + F&lt;/math&gt;

&lt;math&gt;A, B, C, D, E, F&lt;/math&gt; are 6 unknowns.

&lt;math&gt;x^5(A) + x^4(B) + x^3(C) + x^2(D) + x(E) + 1(F) - y = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code:

pt1 = x1,y1 = -8,0
pt2 = x2,y2 = -6,0
pt3 = x3,y3 = -3,0
pt4 = x4,y4 = 1,0
pt5 = x4,y5 = 3,0
pt6 = x6,y6 = 5,10

input = []

for pt in (pt1,pt2,pt3,pt4,pt5,pt6) :
    x,y = pt
    input += [[ x**5, x**4, x**3, x**2, x, 1, -y  ]]

print (input)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
[[-32768, 4096, -512, 64, -8, 1,   0],
 [ -7776, 1296, -216, 36, -6, 1,   0],
 [  -243,   81,  -27,  9, -3, 1,   0],
 [     1,    1,    1,  1,  1, 1,   0],
 [   243,   81,   27,  9,  3, 1,   0],
 [  3125,  625,  125, 25,  5, 1, -10]]
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
result = solveMbyN (input)

s1 = 'result'
print (s1, eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
result (0.0010926573426573423, 0.014204545454545447, 0.027316433566433533, 
       -0.18028846153846156,  -0.3343531468531468,   0.47202797202797203)
&lt;/syntaxhighlight&gt;
From these results the following ratios may be deduced:

&lt;math&gt;\frac{1}{A} = 915.2;\ &lt;/math&gt;
&lt;math&gt;\frac{B}{A} = 13;\ &lt;/math&gt;
&lt;math&gt;\frac{C}{A} = 25;\ &lt;/math&gt;
&lt;math&gt;\frac{D}{A} = -165;\ &lt;/math&gt;
&lt;math&gt;\frac{E}{A} = -306;\ &lt;/math&gt;
&lt;math&gt;\frac{F}{A} = 432.&lt;/math&gt;


&lt;math&gt;y = f(x) = \frac{x^5 + 13x^4 + 25x^3 - 165x^2 - 306x + 432}{915.2}&lt;/math&gt;

===Resistive network===
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[[File:1127network01.png|thumb|400px|'''
Figure 1. Diagram of resistive network containing 8 resistors.'''
]]
A resistive network containing 8 resistors is connected as shown in Figure 1.

What is resistance &lt;math&gt;R&lt;/math&gt; between points &lt;math&gt;P_1, P_3?&lt;/math&gt;
{{RoundBoxBottom}}
====Solve for 8 Branch Currents====
{{RoundBoxTop|theme=2}}
[[File:1127network02.png|thumb|400px|'''
Figure 2. Diagram of resistive network showing all branch currents.'''
&lt;/br&gt;
&lt;/br&gt;
At any point to which 3 or more conductors are connected, sum of currents = 0.
&lt;/br&gt;
At point &lt;math&gt;P_4&lt;/math&gt; currents &lt;math&gt;i_1, i_7&lt;/math&gt; flow towards point; current &lt;math&gt;i_4&lt;/math&gt;
flows away from point.
&lt;/br&gt;
&lt;math&gt;i_1 + i_7 - i_4 = 0.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
In any closed loop sum of voltages = 0.
&lt;/br&gt;
In loop containing points &lt;math&gt;P_1, P_2&lt;/math&gt; voltages &lt;math&gt;e_2, e_8&lt;/math&gt; are clockwise; voltage &lt;math&gt;e_3&lt;/math&gt;
is counter-clockwise.
&lt;math&gt;&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e_2 + e_8 - e_3 = 0.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Direction of flow through 
&lt;math&gt;r_7, r_8&lt;/math&gt; is assumed and is subject to correction.
]]
Voltage across &lt;math&gt;r_1:&lt;/math&gt;

Using &lt;math&gt;E = IR,\ e_1 = i_1\cdot r_1 = r_1\cdot a.&lt;/math&gt;


Similarly:

&lt;math&gt;e_2 = r_2\cdot b.&lt;/math&gt;

&lt;math&gt;e_3 = r_3\cdot c.&lt;/math&gt;

&lt;math&gt;\dots\dots&lt;/math&gt;

&lt;math&gt;e_8 = r_8\cdot h.&lt;/math&gt;


Build a matrix size 8 by 9 which will be input to function solveMbyN().

&lt;syntaxhighlight lang=python&gt;
# Python code:

r1,r2,r3,r4,r5,r6,r7,r8 = 10,20,30,40,50,60,70,80

input = []

# e1 = e2 + e7
# 10a = 20b + 70g
#          10a - 20b + 0c + 0d + 0e + 0f - 70g + 0h + 0 = 0
input += [[r1, - r2,   0,   0,   0,   0, - r7,   0,   0]]

# e3 = e2 + e8
# 30c = 20b + 80h
#          0a - 20b + 30c + 0d + 0e + 0f + 0g - 80h + 0 = 0
input += [[0, - r2,   r3,   0,   0,   0,   0, - r8,   0]]

# e5 = e7 + e4
# 50e = 70g + 40d
#          0a + 0b + 0c - 40d + 50e + 0f - 70g + 0h + 0 = 0
input += [[0,   0,   0, - r4,   r5,   0, - r7,   0,   0]]

# e5 = e8 + e6
# 50e = 80h + 60f
#          0a + 0b + 0c + 0d + 50e - 60f + 0g - 80h + 0 = 0
input += [[0,   0,   0,   0,   r5, - r6,   0, - r8,   0]]

# i7 + i5 + i8 = i2
# g + e + h = b
#          0a - 1b + 0c + 0d + 1e + 0f + 1g + 1h + 0 = 0
input += [[0 ,- 1,   0,   0,   1,   0,   1,   1,   0]]

# i4 = i1 + i7
# d = a + g
#          -1a + 0b + 0c + 1d + 0e + 0f - 1g + 0h + 0 = 0
input += [[-1,   0,   0,   1,   0,   0, - 1,   0,   0]]

# i6 = i3 + i8
# f = c + h
#          0a + 0b - 1c + 0d + 0e + 1f + 0g - 1h + 0 = 0
input += [[0,   0, - 1,   0,   0,   1,   0, - 1,   0]]

# Total input current = 1
# a + b + c = 1
#          1a + 1b + 1c + 0d + 0e + 0f + 0g + 0h - 1 = 0
input += [[1,   1,   1,   0,   0,   0,   0,   0, - 1]]
&lt;/syntaxhighlight&gt;
This last entry can contain almost any arbitrary values. For example:
&lt;syntaxhighlight lang=python&gt;
# Python code:

# i7 = 2.3
input += [[0,   0,   0,   0,   0,   0,   1,   0, - 2.3]]

# e5 = 1.9
input += [[0,   0,   0,   0,   r5,   0,   0,   0, - 1.9]]
&lt;/syntaxhighlight&gt;
Changing this last entry changes all values of &lt;math&gt;e_x, i_x.&lt;/math&gt; However, the ratio &lt;math&gt;\frac{e_x}{i_x} = r_x&lt;/math&gt;
remains constant.
{{RoundBoxTop|theme=3}}
input is matrix of size 8 by 9:
&lt;syntaxhighlight&gt;
[
    [10, -20,  0,   0,  0,   0, -70,   0,  0],  # e1 = e2 + e7,      or r1(i1) - r2(i2) - r7(i7) = 0
    [ 0, -20, 30,   0,  0,   0,   0, -80,  0],  # e3 = e2 + e8,      or r3(i3) - r2(i2) - r8(i8) = 0
    [ 0,   0,  0, -40, 50,   0, -70,   0,  0],  # e5 = e4 + e7,      or r5(i5) - r4(i4) - r7(i7) = 0
    [ 0,   0,  0,   0, 50, -60,   0, -80,  0],  # e5 = e6 + e8,      or r5(i5) - r6(i6) - r8(i8) = 0
    [ 0,  -1,  0,   0,  1,   0,   1,   1,  0],  # i2 = i5 + i7 + i8, or 1(i5) + 1(i7) + 1(i8) - 1(i2) = 0
    [-1,   0,  0,   1,  0,   0,  -1,   0,  0],  # i4 = i1 + i7,      or 1(i4) - 1(i1) - 1(i7) = 0
    [ 0,   0, -1,   0,  0,   1,   0,  -1,  0],  # i6 = i3 + i8,      or 1(i6) - 1(i3) - 1(i8) = 0
    [ 1,   1,  1,   0,  0,   0,   0,   0, -1]   # i1 + i2 + i3 = 1,  or 1(i1) + 1(i2) + 1(i3) - 1 = 0
]
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
i1,i2,i3,i4,i5,i6,i7,i8 = values_of_i = solveMbyN (input)

s1 = 'values_of_i' ; print(s1,eval(s1))
s1 = 'i1 + i2 + i3' ; print(s1,eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
values_of_i (0.45727389222364606,  0.3065353746543468,  0.23619073312200717, 
             0.4350171983543536,   0.31685438726647336, 0.24812841437917316, 
            -0.022256693869292507, 0.011937681257165982)
i1 + i2 + i3 1.0
&lt;/syntaxhighlight&gt;
&lt;math&gt;i_7&lt;/math&gt; has negative value. Reverse &lt;math&gt;i_7&lt;/math&gt; to make all branch currents positive.
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====Make all Branch Currents positive====
{{RoundBoxTop|theme=2}}
[[File:1127network03.png|thumb|400px|'''
Figure 3. Diagram of resistive network showing all branch currents positive.'''
]]
Make &lt;math&gt;i_7&lt;/math&gt; positive and check results.

&lt;syntaxhighlight lang=python&gt;
# Python code

i7 *= -1

values_of_e = e1,e2,e3,e4,e5,e6,e7,e8 = [ 
    eval(s1) 
    for s in '12345678' 
    for s1 in [ 'i' + s + '*r' + s ]
]
s1 = 'values_of_e'
print(s1,eval(s1))
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
values_of_e [ 4.572738922236461,  6.130707493086937,
              7.085721993660215, 17.400687934174144,
             15.842719363323669, 14.88770486275039, 
              1.5579685708504756, 0.9550145005732785]
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

t1 = (
'e1+e7-e2',              # e1 + e7 should equal e2
'e2+e8-e3',              # e2 + e8 should equal e3
'e7+e5-e4',              # e7 + e5 should equal e4
'e8+e6-e5',              # e8 + e6 should equal e5

'e1+e4-(e2+e5)',         # e1 + e4 should equal e2 + e5
'e1+e4-(e3+e6)',         # e1 + e4 should equal e3 + e6

'e1+e7+e8-e3',           # e1 + e7 + e8 should equal e3
'e7+e8+e6-e4',           # e7 + e8 + e6 should equal e4

'i1-i7-i4',              # i1 should equal i7 + i4
'i6-i3-i8',              # i6 should equal i3 + i8
'i2+i7-(i8+i5)',         # i2 + i7 should equal i8 + i5
'i1+i2+i3 - (i4+i5+i6)', # Total input current should
                         # equal total output current.
)

for s1 in t1 :
    print(s1,eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
e1+e7-e2             -8.881784197001252e-16
e2+e8-e3              0.0
e7+e5-e4              0.0
e8+e6-e5              0.0

e1+e4-(e2+e5)         0.0
e1+e4-(e3+e6)         0.0

e1+e7+e8-e3          -8.881784197001252e-16
e7+e8+e6-e4           0.0

i1-i7-i4             -5.551115123125783e-17
i6-i3-i8              6.938893903907228e-18
i2+i7-(i8+i5)         0.0
i1+i2+i3 - (i4+i5+i6) 0.0
&lt;/syntaxhighlight&gt;
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====Compute R====
{{RoundBoxTop|theme=8}}
&lt;syntaxhighlight lang=python&gt;
# Python code

E1 = e3+e6
I1 = i1 + i2 + i3
R1 = E1/I1
s1 = 'R1' ; print(s1,eval(s1))

E2 = e1 + e7 + e5
I2 = i4 + i5 + i6
R2 = E2/I2
s1 = 'R2' ; print(s1,eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
R1 21.973426856410605
R2 21.973426856410605
&lt;/syntaxhighlight&gt;
&lt;math&gt;R = R_1 = R_2&lt;/math&gt;
{{RoundBoxBottom}}

==Solving big matrices==

A big matrix is one of size greater than 10 by 11.

With each recursive call of solveMbyN() the size of each value in decimal digits can theoretically double.
Python's integer math enjoys infinite precision. If your original matrix is of size 32 by 33, 
and each value in the matrix is an int of 1 decimal digit,
function solve2by3() can be called with ints of size 2**30 (1,073,741,824) decimal digits.

Floats can be used instead of ints, but the limited precision of floats may not provide a desirable level
of accuracy in the result.

Python's decimal objects are a good compromise and function reduceRow() above is an attempt to keep the size 
of each member manageable.

Function reduceRow() works well. However, as with all operations involving python's decimal objects, you need to pay
careful attention to precision and accuracy of the results.

On my Mac the following python code generates a matrix of size 100 by 101 and calculates the result containing 
100 values in about 1.5 seconds, including the time to generate 10,100 random numbers, each containing up to 12 
decimal digits with the decimal point in a random position, and including the time to test output over 100 rows 
to verify that all calculated values of the solution satisfy each row.

In function solveMbyN() above find line:
&lt;syntaxhighlight lang=python&gt;
if 0 : # For matrices greater than 10 by 11 enable this piece of code.
&lt;/syntaxhighlight&gt;
Change it to:
&lt;syntaxhighlight lang=python&gt;
if 1 : # For matrices greater than 10 by 11 enable this piece of code.
&lt;/syntaxhighlight&gt;
Then:
&lt;syntaxhighlight lang=python&gt;
from random import getrandbits
from decimal import *
import sys
getcontext().prec=50 # Set precision to 50.

numRows=100

def randomNumber():
# 1 invocation in 256 returns 0.
    if not (getrandbits(10) &amp; 0xFF) : return Decimal(0)
    return [ w
             for q in [ getrandbits(10) &amp; 1]
             for sign in [ (-1,1)[q] ]
             for numberOfDecimalPlaces in [ getrandbits(10) &amp; 0xF ]
             for s1 in [ str(getrandbits(50))[-12:] ]
             for s2 in [ '0'*12+s1 ]
             for posn in [ len(s2)-numberOfDecimalPlaces ]
             for w in [ sign*Decimal(s2[:posn]+'.'+s2[posn:]) ]
           ][0]

data = [[ randomNumber() for p in range(numRows+1) ]
        for p in range (numRows)
       ]

datan = sorted([ v  for row in data for v in row if v &lt; 0 ])
datap = sorted([ v  for row in data for v in row if v &gt;= 0 ])
print ('A small sample of the random numbers in data:')
print ('+ve values:',len(datap), ',', datap[:2],'\n   ',datap[-2:])
print ('-ve values:',len(datan), ',', datan[:2],'\n   ',datan[-2:])

output = solveMbyN(data)

print ('A small sample of the solutions:')
print ('output[0]  =', output[0])
print ('output[19] =', output[19])
print ('output[59] =', output[59])
print ('output[99] =', output[99])
&lt;/syntaxhighlight&gt;
&lt;pre&gt;
A small sample of the random numbers in data:
+ve values: 5021 , [Decimal('1.16871265E-7'), Decimal('1.73721245E-7')]
    [Decimal('998523464710'), Decimal('999768605679')]
-ve values: 5079 , [Decimal('-991079944209'), Decimal('-989786083110')]
    [Decimal('-4.10272824E-7'), Decimal('-2.38664537E-7')]
    
A small sample of the solutions:
output[0]  = 0.43689400018920695253771832432651757885163362928745
output[19] = 0.19867480862268284151047885891372314311902973127033
output[59] = 0.46169681824826309421940885550155275946668017604646
output[99] = -0.020598220802233733529683040085023443421113627790464
&lt;/pre&gt;
===Testing results===
Data input to function solveMbyN() is an array of 100 rows, each row containing 101 numbers.
&lt;pre&gt;
[
[v0_0, v0_1, v0_2, ..... v0_98,v0_99,v0_100],
.......
[v99_0,v99_1,v99_2, ...... v99_98,v99_99,v99_100],]
]
&lt;/pre&gt;
Data received from function solveMbyN() is an array of 100 numbers.
&lt;pre&gt;
[ s0,s1,s2, ...... s98,s99 ]
&lt;/pre&gt;
The first row is tested with the solutions by;
&lt;pre&gt;
L2 = [ v0_0*s0, v0_1*s1, v0_2*s2, ..... v0_98*s98,v0_99*s99,v0_100 ]
&lt;/pre&gt;
sum is the sum of all items in L2.

sum is appended to L1 and the process is repeated for all 100 rows.

&lt;syntaxhighlight lang=python&gt;
L1 = []
for row in data :
# a, b, c, d, e, f, g ....... # row
# u, v, w, x, y, z            # output
        L2 = [ row[p]*t1[p] for t1 in (output+(1,),) for p in range (0, len(row)) ]
# L2 = [a*u , b*v , c*w , d*x , e*y , f*z , g]
        sum = [ sum for sum in [0] for p in L2 for sum in [sum+p] ][-1]
# sum = [a*u, a*u + b*v, a*u + b*v + c*w, a*u + b*v + c*w + d*x, a*u + b*v + c*w + d*x + e*y,
#        a*u + b*v + c*w + d*x + e*y + f*z, a*u + b*v + c*w + d*x + e*y + f*z + g][-1]
# sum = a*u + b*v + c*w + d*x + e*y + f*z + g
# sum is the sum of all items in L2
        L1 += [abs(sum)]

L1a = sorted(L1)
print (len(L1a), L1a[0], L1a[-1])
&lt;/syntaxhighlight&gt;
Ideally sum should be zero.

In practice it's extremely unlikely that sum will be zero. My results typically gave values close to 
&lt;pre&gt;
100 4.1065149609E-38 9.6425614873452398368906E-25
&lt;/pre&gt;
The worst of the results above was 23 zeroes after the decimal point.

Better results can be achieved by increasing precision.
===Cubic Resistive Network===
{{RoundBoxTop|theme=2}}
[[File:1129network01.png|thumb|400px|'''
Figure 1. Diagram of resistive network containing 12 resistors.'''
&lt;/br&gt;
Blue arrows show assumed direction of current.
]]
A resistive network containing 12 resistors is connected as shown in Figure 1.


The network is called &quot;cubic&quot; because, in 3 dimensions, each resistor is located on one
edge of a cube.


What is resistance &lt;math&gt;R&lt;/math&gt; between points &lt;math&gt;P_1, P_2?&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
# Python code:

values_of_r = r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12 = 10,20,30,40,50,60,70,80,90,100,110,120
&lt;/syntaxhighlight&gt;

{{RoundBoxBottom}}
====Solve for 12 Branch Currents====
=====Create matrix 12 by 13=====
&lt;syntaxhighlight lang=python&gt;
# Python code:
input = [
[10, 20, -30, -40,   0,  0,   0,   0,  0,    0,   0,    0,    0],  # e1 + e2 = e3 + e4
[ 0,  0,   0,   0,  50, 60, -70, -80,  0,    0,   0,    0,    0],  # e5 + e6 = e7 + e8
[ 0,  0,   0,  40,   0,  0,   0, -80,  0,    0, 110, -120,    0],  # e11 + e4 = e8 + e12
[10,  0,   0,   0, -50,  0,   0,   0, 90, -100,   0,    0,    0],  # e9 + e1 = e5 + e10
[ 0,  0,   0,   0,   1, -1,   0,   0,  0,   -1,   0,    0,    0],  # i5 = i10 + i6
[ 0,  0,   0,   0,   0,  0,   1,  -1,  0,    0,  -1,    0,    0],  # i7 = i11 + i8
[-1,  0,  -1,   0,   0,  0,   0,   0,  1,    0,   0,    0,    0],  # i9 = i1 + i3
[ 0,  0,  -1,   1,   0,  0,   0,   0,  0,    0,  -1,    0,    0],  # i4 = i3 + i11
[-1,  1,   0,   0,   0,  0,   0,   0,  0,   -1,   0,    0,    0],  # i2 = i1 + i10
[ 0,  0,   0,   0,   0, -1,   0,  -1,  0,    0,   0,    1,    0],  # i12 = i6 + i8
[ 0, -1,   0,  -1,   1,  0,   1,   0,  1,    0,   0,   -1,    0],  # i9 + i5 + i7 = i2 + i4 + i12
[ 0,  0,   1,   0,   0,  0,   0,   0,  0,    0,   0,    0, -1.6]  # i3 = 1.6
]

i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12 = values_of_i = solveMbyN (input)
s1 = 'values_of_i'
print(s1,eval(s1))
&lt;/syntaxhighlight&gt;
This matrix failed:
&lt;syntaxhighlight&gt;
solve2by3() : empty row in input.
  input =
    (0, 0, 0)
    (90533116137774317568000000000000000000000000000000000000000000, -84449318308603494400000000000000000000000000000000000000000000, 1.4228848407261846e+61)
checkDirectionNumbers() : 2 rows parallel, 1 and 2.
  input of solve3by4() =
    [38760268800000000000000000000, 593753233920000000000000000000, -569385344000000000000000000000, 0]
    [620164300800000000000000000000000000, 9500051742720000000000000000000000000, -9110165504000000000000000000000000000, 0]
    [153839206400000000000000000000000, 20882470400000000000000000000000, -81126144000000000000000000000000, -3.67098806272e+32]
&lt;/syntaxhighlight&gt;

=====Try again=====
&lt;syntaxhighlight lang=python&gt;
# Python code:
input = [
  [10, 20, -30, -40,   0,  0,   0,   0,  0,    0,   0,    0,    0],  # e1 + e2 = e3 + e4
  [ 0,  0,   0,   0,  50, 60, -70, -80,  0,    0,   0,    0,    0],  # e5 + e6 = e7 + e8
  [ 0,  0,   0,  40,   0,  0,   0, -80,  0,    0, 110, -120,    0],  # e11 + e4 = e8 + e12
  [10,  0,   0,   0, -50,  0,   0,   0, 90, -100,   0,    0,    0],  # e9 + e1 = e5 + e10
  [ 0,  0,   0,   0,   1, -1,   0,   0,  0,   -1,   0,    0,    0],  # i5 = i10 + i6
  [ 0,  0,   0,   0,   0,  0,   1,  -1,  0,    0,  -1,    0,    0],  # i7 = i11 + i8
  [-1,  0,  -1,   0,   0,  0,   0,   0,  1,    0,   0,    0,    0],  # i9 = i1 + i3
  [ 0,  0,  -1,   1,   0,  0,   0,   0,  0,    0,  -1,    0,    0],  # i4 = i3 + i11
  [-1,  1,   0,   0,   0,  0,   0,   0,  0,   -1,   0,    0,    0],  # i2 = i1 + i10
  [ 0,  0,   0,   0,   0, -1,   0,  -1,  0,    0,   0,    1,    0],  # i12 = i6 + i8
 #[ 0, -1,   0,  -1,   1,  0,   1,   0,  1,    0,   0,   -1,    0],  # i9 + i5 + i7 = i2 + i4 + i12 DELETED.
  [10, 20,   0,   0,   0,  0, -70, -80, 90,    0,   0, -120,    0],  # e9 + e1 + e2 = e7 + e8 + e12 ADDED.
  [ 0,  0,   1,   0,   0,  0,   0,   0,  0,    0,   0,    0, -1.6]   # i3 = 1.6
]

import decimal
dD = decimal.Decimal
dgt = decimal.getcontext()
Precision = dgt.prec = 30
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))

# Convert all values in input to decimal objects with precision of 30.

input = [ [ dD(str(p)) for p in v  ] for v in input ]

i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12 = values_of_i = solveMbyN (input)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
# values_of_i

5.5027171492204899777282850777     9.3809275973899113038721525414     1.5999999999999999999999999999  # i3 should be 1.6.
4.8661430860000781463681475402     6.12901340210213730316883522816    2.25080295393271597702496776458
4.68526862814050716992927753670    1.41912554214042902356112999643    7.10271714922048997772828507766
3.87821044816942132614386746358    3.26614308600007814636814754027    3.66992849607314500058609776103
&lt;/syntaxhighlight&gt;

====Compute R====
{{RoundBoxTop|theme=8}}
&lt;syntaxhighlight lang=python&gt;
# python code

values_of_e = e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12 = [ (i*r) for (i,r) in zip(values_of_i, values_of_r) ]
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
values_of_e
55.0271714922048997772828507770    187.618551947798226077443050828    47.9999999999999999999999999970 
194.645723440003125854725901608    306.450670105106865158441761408    135.048177235962958621498065875
327.968803969835501895049427569    113.530043371234321884890399714    639.244543429844097995545656989
387.821044816942132614386746358    359.275739460008596100496229430    440.391419528777400070331731324
&lt;/syntaxhighlight&gt;
&lt;math&gt;e_3&lt;/math&gt; should be &lt;math&gt;48,\ i_3*r_3&lt;/math&gt; or &lt;math&gt;1.6*30.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
E1 = e5 + e10 + e2
I1 = i9 + i5 + i7
R1 = E1/I1
s1 = 'R1' ; print(s1,eval(s1))

E2 = e7 + e8 - e6 + e10 - e1 + e3 + e4
I2 = i2 + i4 + i12
R2 = E2/I2
s1 = 'R2' ; print(s1,eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
R1 49.2208688540148837936367036806
R2 49.2208688540148837936367036803
&lt;/syntaxhighlight&gt;
Display results with precision of 28:
&lt;syntaxhighlight lang=python&gt;
dgt.prec = 28
R1 += 0 ; R2 += 0
dgt.prec = Precision

s1 = 'R1' ; print(s1,eval(s1))
s1 = 'R2' ; print(s1,eval(s1))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
R1 49.22086885401488379363670368 
R2 49.22086885401488379363670368
&lt;/syntaxhighlight&gt;
&lt;math&gt;R = R_1 = R_2.&lt;/math&gt;
{{RoundBoxBottom}}

====Review====
In matrix all values &lt;math&gt;i_1, i_2, \dots, i_{11}, i_{12}&lt;/math&gt; and &lt;math&gt;e_1, e_2, \dots, e_{11}, e_{12}&lt;/math&gt; are included.


Testing was done with the following lines substituted for last line of matrix:
&lt;syntaxhighlight lang=python&gt;
# python code
[ 0,  0,   0,    0,   0,  0,   1,    0,  0,    0,   0,    0, -3.15]  # i7 = 3.15
[ 0,  0,   0,   r4,   0,  0,   0,    0,  0,    0,   0,    0, -6   ]  # e4 = 6
[ 0,  0,   r3,   0,   0,  0,   0,   r8,  0,    0,   0,    0, -5   ]  # e3 + e8 = 5
&lt;/syntaxhighlight&gt;
All tests produced a consistent value of &lt;math&gt;R.&lt;/math&gt;

====Checking====
=====Examples of current nodes=====

{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0101network01.png|&lt;small&gt;&lt;math&gt;i_1 + i_{10} = i_2&lt;/math&gt;&lt;/small&gt;
File:0101network02.png|&lt;small&gt;&lt;math&gt;i_6 + i_8 = i_{12}&lt;/math&gt;&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}

=====Examples of voltage loops=====

{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0108network00.png|&lt;small&gt;Top and Bottom.&lt;math&gt;e_1 + e_2 - e_4 - e_3 = 0&lt;/math&gt;&lt;math&gt;e_5 + e_6 - e_8 - e_7 = 0&lt;/math&gt;&lt;/small&gt;
File:0108network01.png|&lt;small&gt;Two sides in background.&lt;math&gt;e_5 + e_{10} - e_1 - e_9 = 0&lt;/math&gt;&lt;math&gt;e_6 + e_{12} - e_2 - e_{10} = 0&lt;/math&gt;&lt;/small&gt;
File:0108network02.png|&lt;small&gt;Two sides in foreground.&lt;math&gt;e_7 + e_{11} - e_3 - e_9 = 0&lt;/math&gt;&lt;math&gt;e_8 + e_{12} - e_4 - e_{11} = 0&lt;/math&gt;&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}
=====Python code=====
&lt;syntaxhighlight lang=python&gt;
t1 = (
# 3 nodes on top
'i1 + i10 - i2',
'i1 + i3 - i9',
'i3 + i11 - i4',

# 3 nodes on bottom
'i10 + i6 - i5',
'i11 + i8 - i7',
'i6 + i8 - i12',

# Total input current equals total output current.
'i5 + i7 + i9 - i2 - i4 - i12',

# Voltage loops
# top
'e1 + e2 - e4 - e3',

# bottom
'e5 + e6 - e8 - e7',

# 2 sides in background
'e9 + e1 - e10 - e5',
'e10 + e2 - e12 - e6',

# 2 sides in foreground
'e9 + e3 - e11 - e7',
'e11 + e4 - e12 - e8',

# Some elaborate loops.
'e8 - e6 + e10 + e2 - e4 - e3 - e9 + e7',
'e10 + e2 - e12 - e8 + e11 - e3 - e9 + e5',
)
&lt;/syntaxhighlight&gt;
Result of each of the above calculations should be &lt;math&gt;0.&lt;/math&gt;

Because of small rounding errors, result may not be exactly &lt;math&gt;0.&lt;/math&gt;

See values_of_i and values_of_e above.

This code verifies that result is close enough to &lt;math&gt;0&lt;/math&gt; to be acceptable.

For example:

&lt;math&gt;\text{result} = e_{10} + e_2 - e_{12} - e_8 + e_{11} - e_3 - e_9 + e_5.&lt;/math&gt;

&lt;math&gt;\text{v1} = e_{10} + e_2 + e_{11} + e_5,&lt;/math&gt; sum of positive values.

&lt;math&gt;\text{status = (abs(result)} &lt; \text{(v1}*\text{Tolerance)). status}&lt;/math&gt; should be &lt;math&gt;\text{True.}&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code

import re

for str1 in t1 :
    str2 = re.sub ('\+', ';+', str1)
    str2 = re.sub ('\-', ';-', str2)
    L1 = str2.split(';')
    positives = ''.join([ v for v in L1 if '-' not in v ])
    result = eval(str1)
    v1 = eval( positives )
    status = (abs(result) &lt; (v1*Tolerance))
    str3 = (str1+(' '*40))[:42]
    str4 = ((' '*10) + str(result))[-10:]
    str5 = '{}{}    {}'.format(str3,str4,status)
    print ( str5 )
&lt;/syntaxhighlight&gt;

{| class=&quot;wikitable&quot;
|- 
! Calculation || Result !! Result Acceptable
|-
| &lt;math&gt; i_1 + i_{10} - i_2 &lt;/math&gt;
| &lt;math&gt; -1.2E-28 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; i_1 + i_3 - i_9 &lt;/math&gt;
| &lt;math&gt; -6E-29 &lt;/math&gt; 
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; i_3 + i_{11} - i_4 &lt;/math&gt;
| &lt;math&gt; -3E-29 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; i_{10} + i_6 - i_5 &lt;/math&gt;
| &lt;math&gt; 0E-29 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt; 
|-
| &lt;math&gt; i_{11} + i_8 - i_7 &lt;/math&gt;
| &lt;math&gt; 0E-29 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; i_6 + i_8 - i_{12} &lt;/math&gt;
| &lt;math&gt; -2E-29 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-  
| &lt;math&gt; i_5 + i_7 + i_9 - i_2 - i_4 - i_{12} &lt;/math&gt;
| &lt;math&gt; -3E-29 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; e_1 + e_2 - e_4 - e_3 &lt;/math&gt;
| &lt;math&gt; 0E-28 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-  
| &lt;math&gt; e_5 + e_6 - e_8 - e_7 &lt;/math&gt;
| &lt;math&gt; 0E-27 &lt;/math&gt; 
| &lt;math&gt;\text{True}&lt;/math&gt;
|-  
| &lt;math&gt; e_9 + e_1 - e_{10} - e_5 &lt;/math&gt;
| &lt;math&gt; 0E-27 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; e_{10} + e_2 - e_{12} - e_6 &lt;/math&gt;
| &lt;math&gt; -1.3E-26 &lt;/math&gt; 
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; e_9 + e_3 - e_{11} - e_7 &lt;/math&gt;
| &lt;math&gt; -1.3E-26 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; e_{11} + e_4 - e_{12} - e_8 &lt;/math&gt;
| &lt;math&gt; 0E-27 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; e_8 - e_6 + e_{10} + e_2 - e_4 - e_3 - e_9 + e_7 &lt;/math&gt;
| &lt;math&gt; 0E-27 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|-
| &lt;math&gt; e_{10} + e_2 - e_{12} - e_8 + e_{11} - e_3 - e_9 + e_5 &lt;/math&gt;
| &lt;math&gt; 0E-27 &lt;/math&gt;
| &lt;math&gt;\text{True}&lt;/math&gt;
|}
===Big Matrix 64 by 65===
{{RoundBoxTop|theme=2}}
[[File:0706matrix64_01.png|thumb|400px|'''Diagram of resistive network containing 64 resistors.'''
&lt;/br&gt;
Positive current flow is assumed to be from bottom to top or from left to right.
]]
A network containing 64 resistors is connected as shown in diagram.

What is resistance R between points P1, P2?

&lt;syntaxhighlight lang=python&gt;
# python code
values_of_R = (
    R10, R11, R12, R13, R14, R15, R16, R17, R18, R19, 
    R20, R21, R22, R23, R24, R25, R26, R27, R28, R29, 
    R30, R31, R32, R33, R34, R35, R36, R37, R38, R39,
    R40, R41, R42, R43, R44, R45, R46, R47, R48, R49, 
    R50, R51, R52, R53, R54, R55, R56, R57, R58, R59, 
    R60, R61, R62, R63, R64, R65, R66, R67, R68, R69,
    R70, R71, R72, R73, 
) = [ v for v in range (100,731,10) ]
&lt;/syntaxhighlight&gt;
While this resistive circuit may be very theoretical, it lends itself well to the creation of a big matrix, 64 by 65, meaning that there are 64
resistors and 64 simultaneous equations to be solved.
{{RoundBoxBottom}}
====Create matrix====
An examination of the circuit produces the following conditions:

&lt;syntaxhighlight lang=python&gt;
# python code

iconditions = [
              &quot;+ i10 + i70 - i44&quot; ,        &quot;+ i11 - i10 - i49&quot; ,        &quot;+ i12 - i11 - i54&quot;,
              &quot;+ i13 - i12 - i59&quot; ,        &quot;+ i14 - i13 - i64&quot; ,        &quot;+ i15 + i44 - i43&quot;,
  &quot;+ i16 + i49 - i15 - i48 - i70&quot; ,  &quot;+ i17 + i54 - i16 - i53&quot; ,  &quot;+ i18 + i59 - i17 - i58&quot;,
  &quot;+ i19 + i64 + i71 - i18 - i63&quot; ,        &quot;+ i69 - i19 - i68&quot; ,        &quot;+ i20 + i43 - i42&quot;,
        &quot;+ i21 + i48 - i20 - i47&quot; ,  &quot;+ i22 + i53 - i21 - i52&quot; ,  &quot;+ i23 + i58 - i22 - i57&quot;,
        &quot;+ i24 + i63 - i23 - i62&quot; ,        &quot;+ i68 - i24 - i67&quot; ,        &quot;+ i25 + i42 - i41&quot;,
        &quot;+ i26 + i47 - i25 - i46&quot; ,  &quot;+ i27 + i52 - i26 - i51&quot; ,  &quot;+ i28 + i57 - i27 - i56&quot;,
        &quot;+ i29 + i62 - i28 - i61&quot; ,        &quot;+ i67 - i29 - i66&quot; ,        &quot;+ i30 + i41 - i40&quot;,
  &quot;+ i31 + i46 - i30 - i45 - i72&quot; ,  &quot;+ i32 + i51 - i31 - i50&quot; ,  &quot;+ i33 + i56 - i32 - i55&quot;,
  &quot;+ i34 + i61 + i73 - i33 - i60&quot; ,        &quot;+ i66 - i34 - i65&quot; ,        &quot;+ i36 + i45 - i35&quot;,
              &quot;+ i37 + i50 - i36&quot; ,        &quot;+ i38 + i55 - i37&quot; ,        &quot;+ i39 + i60 - i38&quot;,
              &quot;+ i65 - i39 - i73&quot;
]

sx = 'len(iconditions)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(iconditions) = 34
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
econditions = [
  &quot;+ e40 + e30 - e35 - e45&quot; ,  &quot;+ e41 + e25 - e30 - e46&quot; ,  &quot;+ e42 + e20 - e25 - e47&quot;,
  &quot;+ e43 + e15 - e20 - e48&quot; ,  &quot;+ e44 + e10 - e15 - e49&quot; ,  &quot;+ e45 + e31 - e36 - e50&quot;,
  &quot;+ e46 + e26 - e31 - e51&quot; ,  &quot;+ e47 + e21 - e26 - e52&quot; ,  &quot;+ e48 + e16 - e21 - e53&quot;,
  &quot;+ e49 + e11 - e16 - e54&quot; ,  &quot;+ e50 + e32 - e37 - e55&quot; ,  &quot;+ e51 + e27 - e32 - e56&quot;,
  &quot;+ e52 + e22 - e27 - e57&quot; ,  &quot;+ e53 + e17 - e22 - e58&quot; ,  &quot;+ e54 + e12 - e17 - e59&quot;,
  &quot;+ e55 + e33 - e38 - e60&quot; ,  &quot;+ e56 + e28 - e33 - e61&quot; ,  &quot;+ e57 + e23 - e28 - e62&quot;,
  &quot;+ e58 + e18 - e23 - e63&quot; ,  &quot;+ e59 + e13 - e18 - e64&quot; ,  &quot;+ e60 + e34 - e39 - e65&quot;,
  &quot;+ e61 + e29 - e34 - e66&quot; ,  &quot;+ e62 + e24 - e29 - e67&quot; ,  &quot;+ e63 + e19 - e24 - e68&quot;,
  &quot;+ e64 + e14 - e19 - e69&quot; ,        &quot;+ e44 + e70 - e15&quot; ,        &quot;+ e64 + e14 - e71&quot;,
        &quot;+ e40 + e30 - e72&quot; ,        &quot;+ e60 + e73 - e39&quot;
]

sx = 'len(econditions)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(econditions) = 29
&lt;/syntaxhighlight&gt;
In iconditions and econditions there are 63 conditions that include all values of i and e.
These 63 conditions are used to create matrix.

The 64th condition is added manually.

The matrix is:
&lt;syntaxhighlight lang=python&gt;
matrix = [
  [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,],
  [-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,],
  [0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,1,0,0,0,],
  [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,300,0,0,0,0,-350,0,0,0,0,400,0,0,0,0,-450,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,250,0,0,0,0,-300,0,0,0,0,0,0,0,0,0,0,410,0,0,0,0,-460,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,200,0,0,0,0,-250,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,420,0,0,0,0,-470,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,150,0,0,0,0,-200,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,430,0,0,0,0,-480,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [100,0,0,0,0,-150,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,440,0,0,0,0,-490,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,310,0,0,0,0,-360,0,0,0,0,0,0,0,0,450,0,0,0,0,-500,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,260,0,0,0,0,-310,0,0,0,0,0,0,0,0,0,0,0,0,0,0,460,0,0,0,0,-510,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,210,0,0,0,0,-260,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,470,0,0,0,0,-520,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,160,0,0,0,0,-210,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,480,0,0,0,0,-530,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,110,0,0,0,0,-160,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,490,0,0,0,0,-540,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,320,0,0,0,0,-370,0,0,0,0,0,0,0,0,0,0,0,0,500,0,0,0,0,-550,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,270,0,0,0,0,-320,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,510,0,0,0,0,-560,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,220,0,0,0,0,-270,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,520,0,0,0,0,-570,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,170,0,0,0,0,-220,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,530,0,0,0,0,-580,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,120,0,0,0,0,-170,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,540,0,0,0,0,-590,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,330,0,0,0,0,-380,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,550,0,0,0,0,-600,0,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,280,0,0,0,0,-330,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,560,0,0,0,0,-610,0,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,230,0,0,0,0,-280,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,570,0,0,0,0,-620,0,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,180,0,0,0,0,-230,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,580,0,0,0,0,-630,0,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,130,0,0,0,0,-180,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,590,0,0,0,0,-640,0,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,340,0,0,0,0,-390,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,600,0,0,0,0,-650,0,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,290,0,0,0,0,-340,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,610,0,0,0,0,-660,0,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,240,0,0,0,0,-290,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,620,0,0,0,0,-670,0,0,0,0,0,0,0,],
  [0,0,0,0,0,0,0,0,0,190,0,0,0,0,-240,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,630,0,0,0,0,-680,0,0,0,0,0,0,],
  [0,0,0,0,140,0,0,0,0,-190,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,640,0,0,0,0,-690,0,0,0,0,0,],
  [0,0,0,0,0,-150,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,440,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,700,0,0,0,0,],
  [0,0,0,0,140,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,640,0,0,0,0,0,0,-710,0,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,300,0,0,0,0,0,0,0,0,0,400,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-720,0,0,],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-390,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,600,0,0,0,0,0,0,0,0,0,0,0,0,730,0,],
  [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,],
]

sx = 'len(matrix)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(matrix) = 64
&lt;/syntaxhighlight&gt;
Bottom line of matrix is equivalent to: &lt;math&gt;(1)i10 + (-1) = 0&lt;/math&gt; or &lt;math&gt;i10 = 1.&lt;/math&gt;
====First result====
The following conditions are included for testing:
&lt;syntaxhighlight lang=python&gt;
more_econditions = [
  &quot;+ e49 + e70 - e10&quot;,
  &quot;+ e19 + e69 - e71&quot;,
  &quot;+ e35 + e45 - e72&quot;,
  &quot;+ e65 + e73 - e34&quot;,
] 

extra_test_conditions = [
  &quot;+ e40 + e41 + e42 + e43 + e44 + e10 - e35 - e45 - e46 - e47 - e48 - e49&quot;,
  &quot;+ e45 + e46 + e47 + e48 + e49 + e11 - e36 - e50 - e51 - e52 - e53 - e54&quot;,
  &quot;+ e50 + e51 + e52 + e53 + e54 + e12 - e37 - e55 - e56 - e57 - e58 - e59&quot;,
  &quot;+ e55 + e56 + e57 + e58 + e59 + e13 - e38 - e60 - e61 - e62 - e63 - e64&quot;,
  &quot;+ e60 + e61 + e62 + e63 + e64 + e14 - e39 - e65 - e66 - e67 - e68 - e69&quot;,
  &quot;+ e44 + e10 + e11 + e12 + e13 + e14 - e69 - e15 - e16 - e17 - e18 - e19&quot;,
  &quot;+ e43 + e15 + e16 + e17 + e18 + e19 - e68 - e20 - e21 - e22 - e23 - e24&quot;,
  &quot;+ e42 + e20 + e21 + e22 + e23 + e24 - e67 - e25 - e26 - e27 - e28 - e29&quot;,
  &quot;+ e41 + e25 + e26 + e27 + e28 + e29 - e66 - e30 - e31 - e32 - e33 - e34&quot;,
  &quot;+ e40 + e30 + e31 + e32 + e33 + e34 - e65 - e35 - e36 - e37 - e38 - e39&quot;,
  &quot;+ i35 + i40 + i72 - i14 - i69 - i71&quot;,
  &quot;+ e40 + e41 + e42 + e43 + e44 + e10 + e11 + e12 + e13 + e14 - e35 - e36 - e37 - e38 - e39 - e65 - e66 - e67 - e68 - e69&quot;,
  &quot;+ e40 + e41 + e42 + e43 + e15 + e16 + e17 + e18 + e19 + e69 - e35 - e36 - e37 - e38 - e60 - e61 - e62 - e63 - e64 - e14&quot;,
  &quot;+ e40 + e41 + e42 + e20 + e21 + e22 + e23 + e24 + e68 + e69 - e35 - e36 - e37 - e55 - e56 - e57 - e58 - e59 - e13 - e14&quot;,
  &quot;+ e40 + e41 + e25 + e26 + e27 + e28 + e29 + e67 + e68 + e69 - e35 - e36 - e50 - e51 - e52 - e53 - e54 - e12 - e13 - e14&quot;,
  &quot;+ e40 + e30 + e31 + e32 + e33 + e34 + e66 + e67 + e68 + e69 - e35 - e45 - e46 - e47 - e48 - e49 - e11 - e12 - e13 - e14&quot;
]
&lt;/syntaxhighlight&gt;
Produce results:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    import decimal
    dD = decimal.Decimal
    dgt = decimal.getcontext()
    Precision = dgt.prec = 60                   # Adjust as necessary.
    Tolerance = dD(&quot;1e-&quot; + str(Precision-4))    # Adjust as necessary.
    
    import re # Regular expressions.

def produce_result (input, flag = 0) :
    thisName = 'produce_result (input, flag = {}) :'.format(flag)

    values_of_i = solveMbyN (input)

    (   i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, 
        i20, i21, i22, i23, i24, i25, i26, i27, i28, i29, 
        i30, i31, i32, i33, i34, i35, i36, i37, i38, i39,
        i40, i41, i42, i43, i44, i45, i46, i47, i48, i49, 
        i50, i51, i52, i53, i54, i55, i56, i57, i58, i59, 
        i60, i61, i62, i63, i64, i65, i66, i67, i68, i69,
        i70, i71, i72, i73, 
    ) = values_of_i

    values_of_e = (
        e10, e11, e12, e13, e14, e15, e16, e17, e18, e19, 
        e20, e21, e22, e23, e24, e25, e26, e27, e28, e29, 
        e30, e31, e32, e33, e34, e35, e36, e37, e38, e39,
        e40, e41, e42, e43, e44, e45, e46, e47, e48, e49, 
        e50, e51, e52, e53, e54, e55, e56, e57, e58, e59, 
        e60, e61, e62, e63, e64, e65, e66, e67, e68, e69,
        e70, e71, e72, e73, 
    ) = [ (i*R) for (i,R) in zip (values_of_i, values_of_R) ]

    E1_ = 'e40 + e41 + e42 + e43 + e44 + e10 + e11 + e12 + e13 + e14'
    E1 = eval(E1_)
    I1 = eval('i40 + i72 + i35')
    R1 = E1/I1

    if not flag : return R1
    # Check all conditions.
    # compiled regular expression plus, compiled regular expression minus
    crep,crem = [ re.compile(re.escape(v)) for v in '+-' ]
    # 
    # This code verifies that result of evaluation of condition 
    # is close enough to 0 to be called 0.
    # 
    for condition in (iconditions + econditions + more_econditions + extra_test_conditions):
        str2 = crep.sub(';+', condition)
        str3 = crem.sub(';-', str2)
        positives = [ v for v in str3.split(';') if ('+' in v) ]
        pos_sum = eval(''.join(positives))
        sum = eval(condition)
        # pos_sum - neg_sum = sum
        neg_sum = pos_sum - sum
        min,max = sorted((neg_sum, pos_sum))
        status = (abs(sum) &lt;= (Tolerance*min))
        if not status :
            print (thisName, 'condition failed:')
            print ('   ', condition, sum)
            return None

    return R1

# Convert all values in matrix to Decimal objects
matrix = [ [ dD(str(eval(str(p)))) for p in v  ] for v in matrix ]

enable_reduceRow = 1

R = produce_result (matrix,1) 

sx = 'R' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
R = 723.928575988442547699732563335265663515838075102937503680598
&lt;/syntaxhighlight&gt;
&lt;math&gt;\text{R}&lt;/math&gt; is printed with precision of 60.
====Matrix corrected====
{{RoundBoxTop|theme=2}}
[[File:0710matrix64_01.png|thumb|400px|'''Diagram of network containing 64 resistors'''
&lt;/br&gt;
Diagram has been corrected to show positive direction of current through R70, R73.
]]
Original assumptions were that currrent flow through 64 resistors would be from bottom to top or from left to right.

Examination of results shows that flow through R70, R73 is from right to left. This is reflected in testing below.

Corrected diagram conforms to assumption that all current flow is from bottom towards top or from left to right.

{{RoundBoxBottom}}

&lt;syntaxhighlight lang=python&gt;
number_of_columns = 65
output = []
# 
# Test this matrix 64 times using 
# i10 = 1
# i11 = 1.1
# i12 = 1.2
# .......
# .......
# i70 = -7
# i71 = 7.1
# i72 = 7.2
# i73 = -7.3
# 
for I in range(10, 74):
    new_line = [ dD(0) ] * number_of_columns
    place_in_line = I - 10
    new_line[place_in_line] = dD(1)
    i = dD(I)/10
    if I in (70,73) : new_line[-1] = i
    else : new_line[-1] = -i
    matrix[-1] = new_line
    r = produce_result (matrix,1)
    if r : output += [ r ]
    
sx = 'len(output)' ; print (sx, '=', eval(sx))

# Produce results with slightly reduced precision:

dgt.prec -= 4
set2 = { r+0 for r in output }
dgt.prec += 4
    
len2 = len(set2)
if len2 == 1 :
    r, = set2
    print ('R =', r)
else :
    print (len2, 'values of R:')
    for v in set2 : print ('   ', v)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(output) = 64 
R = 723.92857598844254769973256333526566351583807510293750368
&lt;/syntaxhighlight&gt;
&lt;math&gt;\text{R}&lt;/math&gt; is printed with precision of 56.

With precision of 56 all 64 results are equal.

[[Category:Equations]]</text>
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= South African wasp species of Tribe Oxybelini ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus Belarnoldus Antropov, 2007 ==

Belarnoldus crassus Arnold, 1936 (South Africa)

== Genus Belokohlus Antropov, 2007 ==

Belokohlus ferrieri (Kohl, 1924) (South Africa)

== Genus Belomicrinus Antropov, 2000 ==

Belomicrinus luteosquamatus Antropov, 2000 (Namibia)

Belomicrinus minutissimus (Arnold, 1936) (Namibia)

== Genus Belomicroides Kohl, 1899 ==

Belomicroides arenarius Arnold, 1960 (Zimbabwe)

Belomicroides clypeatus Antropov, 2002 (South Africa)

Belomicroides erythrogaster Antropov, 2002 (Namibia)

Belomicroides marleyi Arnold, 1927 (South Africa)

Belomicroides maximiliani Antropov, 2002 (Namibia)

Belomicroides pictus Arnold, 1927 (South Africa)

Belomicroides pictus chrysoptilus Antropov, 2002 (Namibia)

Belomicroides politus Antropov, 2002 (Namibia)

Belomicroides rift Antropov, 2002 (Kenya)

Belomicroides veronicae Antropov, 2002 (Ethiopia)

Belomicroides woji Antropov, 2002 (Namibia)

== Genus Belomicrus Costa, 1867 ==

Belomicrus mirificus Kohl, 1905 (Ethiopia)

== Genus Brimocelus Arnold, 1927 ==

Brimocelus radiatus (Arnold, 1927) (South Africa)

Brimocelus roosevelti Antropov, 2000 (South Africa)

Brimocelus schwarzi Antropov, 2000 (Namibia)

== Genus Gessus Antropov, 2001 ==

Gessus capensis Antropov, 2001 (South Africa)

== Genus Minimicroides Antropov, 2000 ==

Minimicroides perexiguus Antropov, 2000 (Namibia)

== Genus Nototis Arnold, 1927 ==

Nototis bicornutus Arnold, 1927 (South Africa)

Nototis falcidens Antropov, 2007 (Namibia)

== Genus Oxybelomorpha Brauns, 1897 ==

Oxybelomorpha braunsii (Kohl, 1923) (South Africa)

Oxybelomorpha funesta (Arnold, 1929) (South Africa)

Oxybelomorpha gessi Antropov, 2005 (South Africa)

Oxybelomorpha imitans Antropov, 2005 (South Africa)

Oxybelomorpha kohlii Brauns in Kohl, 1896 (South Africa)

Oxybelomorpha nitens Antropov, 2005 (South Africa)

Oxybelomorpha pseudosordida Antropov, 2005 (Namibia)

Oxybelomorpha pulawskii Antropov, 2005 (South Africa)

Oxybelomorpha rhodesiana (Arnold, 1927) (Zimbabwe)

Oxybelomorpha rubicunda Antropov, 2005 (Namibia)

Oxybelomorpha rufiventris (Arnold, 1936) (South Africa)

Oxybelomorpha separata Antropov, 2005 (South Africa)

Oxybelomorpha sgessae Antropov, 2005 (South Africa)

Oxybelomorpha sordida (Arnold, 1927) (South Africa)

Oxybelomorpha turneri (Arnold, 1927) (South Africa)

Oxybelomorpha wojciechi Antropov, 2005 (Namibia)

== Genus Oxybelus Latreille, 1796 ==

Oxybelus acutissimus Bischoff, 1912 (Democratic Republic of Congo)

Oxybelus acutissimus propinquus Arnold, 1927 (Zimbabwe)

Oxybelus aethiopicus Cameron, 1906 (South Africa)

Oxybelus angustus de Saussure, 1892 (South Africa)

Oxybelus arnoldi Benoit, 1951 (Democratic Republic of Congo)

Oxybelus bechuanae Arnold, 1936 (Botswana)

Oxybelus bicornutus Arnold, 1929 (Namibia, South Africa)

Oxybelus braunsi Arnold, 1927 (South Africa)

Oxybelus congophilus Benoit, 1951 (Democratic Republic of Congo)

Oxybelus coniferus Arnold, 1951 (Ethiopia)

Oxybelus cristatus de Saussure, 1892 (Madagascar)

Oxybelus curviscutis Arnold, 1927 (Zimbabwe)

Oxybelus dissimilis Arnold, 1934 (Zimbabwe)

Oxybelus eburneoguttatus Arnold, 1952 (Zimbabwe)

Oxybelus flavicornis Arnold, 1927 (Zimbabwe)

Oxybelus flavicornis nyassae Arnold, 1927 (Tanzania)

Oxybelus flaviventris Arnold, 1927 (Zimbabwe)

Oxybelus fraudulentus Arnold, 1929 (Namibia)

Oxybelus harraricus Arnold, 1927 (Ethiopia)

Oxybelus hessei Arnold, 1929 (Namibia)

Oxybelus imperialis Gerstaecker, 1867 (South Africa)

Oxybelus lepturus Arnold, 1927 (Zimbabwe)

Oxybelus limatus Arnold, 1927 (Zimbabwe)

Oxybelus lingula Gerstaecker, 1867 (South Africa)

Oxybelus matabele Arnold, 1927 (Zimbabwe)

Oxybelus metopias Kohl, 1894 (Mozambique)

Oxybelus nasutus Bischoff, 1913 (Namibia)

Oxybelus natalensis Arnold, 1927 (South Africa)

Oxybelus neuvillei Magretti, 1908 (Kenya)

Oxybelus pallidus Arnold, 1927 (Ethiopia, Tanzania)

Oxybelus paucipunctatus Arnold, 1927 (Zimbabwe)

Oxybelus peringueyi de Saussure, 1892 (South Africa)

Oxybelus perornatus Arnold, 1945 (Madagascar)

Oxybelus pictus Arnold, 1927 (Zimbabwe)

Oxybelus pilosus Arnold, 1927 (Ethiopia)

Oxybelus rubrocaudatus Arnold, 1927 (Zimbabwe)

Oxybelus ruficaudis Cameron, 1905 (South Africa)

Oxybelus ruficaudis melanarius Arnold, 1927 (South Africa)

Oxybelus solitarius Arnold, 1927 (Zimbabwe)

Oxybelus stevensoni Arnold, 1927 (Zimbabwe)

Oxybelus subcristatus de Saussure, 1892 (Madagascar)

Oxybelus taschenbergi Kohl, 1875 (South Africa)

Oxybelus willowmorensis Arnold, 1927 (South Africa)

Oxybelus woosnami Arnold, 1927 (Botswana, South Africa)

Oxybelus zavattarii Guiglia, 1943 (Ethiopia)

== Genus Wojus Antropov, 1999 ==

Wojus inopinatus Antropov, 1999 (South Africa)&lt;br&gt;
&lt;br&gt;


= South African wasp species of Subtribe Gastrosericina ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus ''Gastrosericus'' ==
There are 25 Afrotropical species; four in South Africa.

== Genus ''Kohliella'' Brauns, 1910 &lt;ref&gt;http://www.biodiversitylibrary.org/page/35572001&lt;/ref&gt;==

There are three species of ''Kohliella''; two are Afrotropical.&lt;ref&gt;https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm&lt;/ref&gt; 

''Kohliella alaris'' is found in South Africa and Zimbabwe; it hunts tree crickets.&lt;ref&gt;Gess, S.K. &amp; Gess, F.W. 2014. Wasps and bees in southern Africa. SANBI Biodiversity Series 24. South African National Biodiversity Institute, Pretoria. p. 71-72. https://archive.org/details/waspsbeesinsouth24gess/page/70/mode/2up&lt;/ref&gt;

== Genus ''Parapiagetia'' ==


== Genus ''Tachytes'' ==
There are 79 Afrotropical species; 15 in South Africa.

== Genus ''Tachysphex '' ==
There are 128 Afrotropical species; 41 in South Africa.

== Genus ''Larropsis '' ==

''Larropsis (Ancistromma) obliqua'' (F. Smith); description in Arnold, 1923b:218 as ''Tachytes obliquus''
== Genus ''Tachytella '' ==
== Genus ''Prosopigastra'' ==
== Genus ''Holotachysphex '' ==
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;


= Southern African wasp species of Tribe Trypoxylini ([[African Arthropods/Crabroninae|Crabronidae]]) =

== Genus ''Pison'' Jurine, 1808 ==

Arnold ([http://www.biodiversitylibrary.org/page/60327574 1924, 1-10]) has a key and descriptions.

*''Pison allonymum'' Schulz, 1906 (South Africa; probably most of southern Africa)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance 1.5 to 2.5 times the diameter of an ocellus;
**Fairly long, whitish or silvery pilosity on head and thorax, more dense on the temples than elsewhere.&lt;ref name=Arnold1924&gt;Arnold, G. (1924) The Sphegidae of South Africa. Part V. Annals of the Transvaal Museum 11:1-4 http://www.biodiversitylibrary.org/page/60327575&lt;/ref&gt;

*''Pison atrum'' (Spinola, 1808:253) described by Cameron as ''Pison montanum'' (Kenya, South Africa, Zambia)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance not greater than the diameter of an ocellus;
**Pronotal collar longer than in ''allonymum''.

*''Pison transvaalense'' Cameron, 1910 (South Africa; probably most of southern Africa to Tanzania and Uganda)
**Head and thorax dull; finely and closely punctured;
**Distance between the posterior ocelli and the eyes is equal to a third to a half of the diameter of the ocellus.


*''Pison auratum'' Shuckard, 1838 (an Australian species; see Pulawski, 2018:85 http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Pulawski_2018.pdf)

*''Pison denticeps'' Cameron, 1910 (South Africa; &quot;Transvaal&quot;. Two cubital cells; he only record seems to be the description)

*''Pison repentinum'' Arnold, 1940 (Zimbabwe)

*''Pison rufitarse'' Arnold, 1944 (Zimbabwe)

*''Pison scruposum'' Arnold, 1955 (Zimbabwe)

== Genus ''Trypoxylon'' Latreille, 1796 ==

*''Trypoxylon abditum'' Arnold, 1924 (South Africa)

*''Trypoxylon algoense'' Arnold, 1924 (South Africa)

*''Trypoxylon arnoldi'' Menke, 1976 (South Africa, Tanzania)

*''Trypoxylon braunsi'' Arnold, 1924 (South Africa)

*''Trypoxylon capense'' Cameron, 1905 (South Africa)

*''Trypoxylon cataractae'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon chirindense'' Arnold, 1936 (Burundi, Democratic Republic of Congo, Rwanda, Uganda, Zimbabwe)

*''Trypoxylon foveatum'' Cameron, 1904 (South Africa)

*''Trypoxylon inconstans'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon infimum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon kohli'' Arnold, 1924 (South Africa)

*''Trypoxylon letiferum'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon lissonotum'' Cameron, 1910 (South Africa)

*''Trypoxylon montivagum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon nodosum'' Arnold, 1944 (Zimbabwe)

*''Trypoxylon punctatissimum'' Arnold, 1924 (South Africa)

*''Trypoxylon stevensoni'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon stroudi'' Gribodo, 1884 (Ethiopia, South Africa, Democratic Republic of Congo)

*''Trypoxylon testaceipes'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon triste'' Arnold, 1924 (Zimbabwe)

= Pompilidae of South Africa =
== South African Pompilidae with fore-wings mainly orange to yellow with fuscous (darker or blackish) wing-tips ==
&lt;gallery mode=packed heights=200&gt;
Inaturalist 258649905 b.jpg
Hemipepsis hilaris - inaturalist 10850475.jpg
Cyphononyx decipiens inat 26259647 b.jpg
Tachypompilus ignitus inaturalist 311015843 02.jpg
Pompilidae 2021 12 12 inaturalist 313386858 04.jpg
Pompilidae 2020 04 13 inaturalist 43563902 06.jpg
&lt;/gallery&gt;
*The extent of the fuscous colour can be limited to the apex of the wing beyond the cells, or extend into the cells to a varying extent.
*
&lt;br&gt;

== South African Pompilidae with fore-wings fuscous (black or very dark) ==
*The wings often have green-blue-violet reflections.
&lt;gallery mode=packed heights=200&gt;
Pompilidae 2019 05 01 2835.jpg|Female ''Batozonellus fuliginosus''
Pompilidae inaturalist 124148802 01.jpg|Female ''Cyphononyx optimus''
Pompilidae 2021 12 18 iNat 316501919 a.jpg|Female ''Cyphononyx obscurus''
Pompilidae 2025 03 14 iNat 266538336 a.jpg|Male ''Hemipepsis vindex''
Pompilidae_2019_05_28_0256.jpg|
Spider-hunting Wasp (Hemipepsis) female (12640106905).jpg|''Hemipepsis'' sp.
&lt;/gallery&gt;

&lt;br&gt;
=== Species  with black antennae, legs, head, thorax and abdomen ===
Some parts may be brown.

*''Java atropos''
*''Cyphononyx obscurus''
*''Hemipepsis vindex''
*''Hemipepsis vespertilio''
*''Hemipepsis braunsi''
*''Batozonellus fuliginosus''
&lt;br&gt;
=== Species with black antennae, head, thorax and abdomen, but legs (or parts of some legs) yellow to red ===
*''Cyphononyx optimus''
*''Paracyphononyx zonatus''
&lt;br&gt;
&lt;br&gt;

== South African Pompilidae with fore-wings mainly hyaline to fuscous-hyaline ==
&lt;gallery mode=packed heights=200&gt;
Pompilidae inaturalist 123577538.jpg
Pompilidae inaturalist 46961473.jpg
Pompilidae iN 144781033 03.jpg

&lt;/gallery&gt;
*With fuscous (darker) wing apex
*One or two fuscous bands (faciated or bifaciated)
*Hyaline parts can be clouded (whiteish clouding) or coloured (yellow-tinted)


&lt;br&gt;
== South African Ceropalinae ==
Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region: [https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 Madl, 2020]
*''Ceropales africana'' Móczar, 1989. - {{font color||yellow|''helvetica'' group}} (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales cribrata cribrata'' A. Costa, 1881; key in Móczár 1986a: 321 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales {{font color||#0f0|(Priesnerius)}} gessi'' Móczar, 1988 (South Africa)
*''Ceropales {{font color||#0f0|(Priesnerius)}} grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales karooensis'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}} (Namibia, South Africa)
*''Ceropales kriechbaumeri'' Magretti, 1884 - {{font color||yellow|''helvetica'' group}} (Burkina Faso, Nigeria, South Africa?, Uganda, Zimbabwe?)
*''Ceropales {{font color||#0f0|(Priesnerius)}} kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Senegal, South Africa, Togo, Zimbabwe) 
*''Ceropales lawrencei'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales picta'' Shuckard, 1837; key in Móczár 1986b: 125 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus'' Cameron, 1904; key in Móczár 1986a: 320 (Lesotho, South Africa)
**''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
**''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
**= Hemiceropales scobinifera (Arnold, 1937): Móczár 1986a: 319
*''Ceropales (Bifidoceropales) sulciscutis'' Cameron, 1910; key in Móczár 1990: 61 (South Africa, Tanzania)
*''Ceropales waltoni'' Arnold, 1959 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989: 12 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
&lt;br&gt;

==Afrotropical Ceropalinae ==

Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region (Madl, 2020).&lt;ref name=Madl2020&gt;Madl, M. (2020). Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region. Zeitschrift der Arbeitsgemeinschaft Österreichischer Entomologen 72: 73-84.
[https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 PDF]&lt;/ref&gt;


Ceropalinae can be defined by:&lt;ref name=Brothers1993&gt;Brothers, D. J. &amp; Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. &amp; Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143&lt;/ref&gt;&lt;ref name=Waichert2015&gt; Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., &amp; Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287. {{doi|10.1111/zoj.12272}} [https://www.researchgate.net/publication/282015793 PDF]&lt;/ref&gt;

== Genera and species of Afrotropical Ceropalinae ==

This list is based on that of [https://www.waspweb.org/Pompiloidea/Pompilidae/Ceropalinae/index.htm '''waspweb'''] with changes following the Catalogue of Life (Kroupa &amp; Schmid-Egger, 2025)&lt;ref name=CoL2025&gt; Kroupa, A. S., &amp; Schmid-Egger, C. (2025). Hymenoptera Information System, Pompilidae of the World (version 2019-09). In O. Bánki, Y. Roskov, M. Döring, G. Ower, D. R. Hernández Robles, C. A. Plata Corredor, T. Stjernegaard Jeppesen, A. Örn, T. Pape, D. Hobern, S. Garnett, H. Little, R. E. DeWalt, J. Miller, T. Orrell, R. Aalbu, J. Abbott, C. Aedo, E. Aescht, et al., Catalogue of Life (Version 2025-07-10). Catalogue of Life Foundation, Amsterdam, Netherlands. https://doi.org/10.48580/dg9ld-4kv &lt;/ref&gt; and [[w:George_Arnold_(entomologist)|papers by Arnold (1932-1962)]].&lt;br&gt;

=== Genus ''Ceropales'' ===
*''Ceropales africana'' Móczar, 1989. (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales arnoldi'' Móczar, 1988 (Namibia)
*''Ceropales atra'' Móczar, 1991 (Botswana)
*''Ceropales cribrata cribrata'' A. Costa, 1881 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales cribrata maculipes'' Móczar, 1986 (Zambia)
*''Ceropales carinitifrons'' Wahis, 1986 (Madagascar)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales dayi'' Móczar, 1989 (Kenya)
*''Ceropales ferrugo'' Móczar, 1989 (Kenya)
*''Ceropales gambiae'' Móczar, 1989 (Burkina Faso, Cameroon, Democratic Republic of Congo, Gambia, Nigeria, Senegal, Sierra Leone)
*''Ceropales gessi'' Móczar, 1988 (South Africa)
*''Ceropales grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales juncoi'' Giner Mari, 1945 (Chad, Egypt, Israel, Pakistan, Somalia, Sudan, Western Sahara)
*''Ceropales karooensis'' Arnold, 1937 (Namibia, South Africa)
*''Ceropales kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Togo, Zimbabwe)
*''Ceropales kriechbaumeri'' Magretti, 1884 (Burkina Faso, Nigeria, South Africa, Uganda, Zimbabwe)
*''Ceropales latifasciatus'' Arnold, 1937 (Ethiopia)
*''Ceropales lawrencei'' Arnold, 1937 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales levipleuris'' Wahis, 1987 (Madagascar)
*''Ceropales maliensis'' Móczar, 1989 (Mali, Senegal)
*''Ceropales maroccana'' Beaumont, 1947 (Burkina Faso, Democratic Republic of Congo, Gambia, Ghana, Ivory Coast, Nigeria, Senegal, Zimbabwe. Also Palaearctic region)
*''Ceropales multipicta'' Arnold, 1937 (Botswana, Namibia)
*''Ceropales picta'' Shuckard, 1837 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus punctulatus'' Cameron, 1904 (Lesotho, South Africa)
*''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
*''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales ruficollis'' Cameron, 1910 (Kenya, Tanzania)
*''Ceropales saegeri'' Móczar, 1988 (Democratic Reublic of Congo)
*''Ceropales senegalensis'' Móczar, 1988 (Burkina Faso, Cameroon, Senegal)
**''Ceropales senegalensis mbouri'' Móczar, 1988 (Senegal)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
*''Ceropales seyrigi'' Wahis, 1987 (Madagascar)
*''Ceropales spinolai'' Móczar, 1988 (Guinea)
*''Ceropales subhelvetica'' Móczar, 1988 (Burkina Faso, Senegal. Also Palaearctic: Israel)
*''Ceropales sulciscutis'' Cameron, 1910 (South Africa, Tanzania)
**''Ceropales sulciscutis raymondi'' Móczar, 1990 (Democratic Republic of Congo)
*''Ceropales variolosus'' Arnold, 1937 (Democratic Republic of Congo, Ghana, Guinea, Mali, Nigeria, Senegal, Sudan, Togo, Uganda)
*''Ceropales waltoni'' Arnold, 1959 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
*''Ceropales yemeni'' Móczar, 1988 (Yemen. Also Palaearctic: Israel, Saudi Arabia)
&lt;br&gt;
=== Genus ''Irenangelus'' ===
*''Irenangelus madescassus'' Wahis, 1988 (Madagascar)
&lt;br&gt;

==Eumeninae==
Photos of ''Antodynerus'' on GBIF:&lt;br&gt;
''alboniger'': https://www.gbif.org/occurrence/1248689053 (CC BY-NC-SA 3.0)&lt;br&gt; 
''hova'': https://www.gbif.org/occurrence/1320165802 (CC0 1.0)&lt;br&gt;
''kelneri'': https://www.gbif.org/occurrence/3762658306 (CC BY-NC-SA 4.0)&lt;br&gt; 
''lugubris'': https://www.gbif.org/occurrence/1248689125 (CC BY-NC-SA 3.0)&lt;br&gt; 
''seyrigi'': https://www.gbif.org/occurrence/1322648015 (CC0 1.0)&lt;br&gt;
''sheffieldi'': https://www.gbif.org/occurrence/1318932924 (CC0 1.0)&lt;br&gt;
''silaos'': https://www.gbif.org/occurrence/1320574593 (CC0 1.0)&lt;br&gt;

==Ants==
'''Subfamilies of Formicidae (WaspWeb)'''

Number of iNaturalist records for subfamilies of Formicidae in Africa (2023-05-23)
Amblyoponinae              7
Dolichoderinae           630
Dorylinae                 1 167
Formicinae            10 396       Camponotus   6 090; Lepisiota 1 046
Myrmicinae              8 484       Crematogaster  1 786;   Pheidole  1 468;   Messor  1 156 
Ponerinae                1 623
Proceratiinae                  3
Pseudomyrmecinae   296


Aenictinae One Afrotropical genus ''Aenictus'' &lt;br&gt;

Aenictogitoninae One Afrotropical genus ''Aenictogiton'' &lt;br&gt;

Amblyoponinae Five Afrotropical genera &lt;br&gt;

Apomyrminae One Afrotropical genus ''Apomyrma'' &lt;br&gt; 

Cerapachyinae Five Afrotropical genera&lt;br&gt;

Dolichoderinae Eight Afrotropical genera&lt;br&gt;

Dorylinae One Afrotropical genus ''Dorylus'' &lt;br&gt;

Formicinae 20 Afrotropical genera&lt;br&gt;

Leptanillinae One Afrotropical genus ''Leptanilla'' &lt;br&gt;

Myrmicinae 37 Afrotropical genera &lt;br&gt;

Ponerinae 18 Afrotropical genera &lt;br&gt;

Proceratiinae Three Afrotropical genera  &lt;br&gt;

Pseudomyrmecinae One Afrotropical genus Tetraponera &lt;br&gt;


&lt;gallery mode=packed heights=200&gt;
Aenictogiton sp.jpg|''Aenictogiton'' sp., Aenictogitoninae 
Apomyrma stygia casent0101444 profile 1.jpg|''Apomyrma stygia'', Apomyrminae 
Cerapachys coxalis casent0173076 profile 1.jpg|''Cerapachys coxalis'', Cerapachyinae 
Cerapachys centurio castype12081-02 profile 1.jpg|''Cerapachys centurio'', Cerapachyinae
Tapinoma subtile casent0132840 dorsal 1.jpg|''Tapinoma subtile'', Dolichoderinae 
Dorylus helvolus, a, Seringveld.jpg|''Dorylus helvolus'', Dorylinae  
Polyrhachis schistacea00.jpg|''Polyrhachis schistacea'', Formicinae 
Anoplolepis custodiens, met prooi, a, Krugersdorp.jpg|''Anoplolepis custodiens'', Formicinae 
AFRICAN THIEF ANT SIX.jpg|''Carebara vidua'', Myrmicinae 
Millipede Hunter Ant (Plectroctena mandibularis) (11904420373).jpg|''Plectroctena mandibularis'', Ponerinae 
Discothyrea hewitti sam-hym-c000061a profile 1.jpg|''Discothyrea hewitti'', Proceratiinae 
Probolomyrmex filiformis casent0102141 profile 1.jpg|''Probolomyrmex filiformis'', Proceratiinae 
Slender Ant (Tetraponera natalensis) (30538051244).jpg|''Tetraponera natalensis'', Pseudomyrmecinae
&lt;/gallery&gt;

== N-P interactions ==
Dai, Z., Liu, G., Chen, H., Chen, C., Wang, J., Ai, S., Wei, D., Li, D., Ma, B., Tang, C., Brookes, P.C. and Xu, J., 2020. Long-term nutrient inputs shift soil microbial functional profiles of phosphorus cycling in diverse agroecosystems. The ISME journal, 14(3), pp.757-770.
'''Abstract'''
Microorganisms play an important role in soil phosphorus (P) cycling and regulation of P availability in agroecosystems. However, the responses of the functional and ecological traits of P-transformation microorganisms to long-term nutrient inputs are largely unknown. This study used metagenomics to investigate changes in the relative abundance of microbial P-transformation genes at four long-term experimental sites that received various inputs of N and P nutrients (up to 39 years). Long-term P input increased microbial P immobilization by decreasing the relative abundance of the P-starvation response gene (phoR) and increasing that of the low-affinity inorganic phosphate transporter gene (pit). This contrasts with previous findings that low-P conditions facilitate P immobilization in culturable microorganisms in short-term studies. In comparison, long-term nitrogen (N) input significantly decreased soil pH, and consequently decreased the relative abundances of total microbial P-solubilizing genes and the abundances of Actinobacteria, Gammaproteobacteria, and Alphaproteobacteria containing genes coding for alkaline phosphatase, and weakened the connection of relevant key genes. This challenges the concept that microbial P-solubilization capacity is mainly regulated by N:P stoichiometry. It is concluded that long-term N inputs decreased microbial P-solubilizing and mineralizing capacity while P inputs favored microbial immobilization via altering the microbial functional profiles, providing a novel insight into the regulation of P cycling in sustainable agroecosystems from a microbial perspective.

==Diptera==
===Wing and leg-waving behavior in flies===
====Food detection====
*''Rhagio lineola'' and ''R. tringarius'' feed on pollen and/or honeydew, which they locate by sweeping their front legs across the surface of leaves. They have a few fine hairs on their front legs, probably for this purpose. Other Rhagionidae do not have these hairs. 
**https://www.researchgate.net/publication/359760392
*It is also possible that some flies sample the air with the chemical sensors on their legs or feet.
**https://bugguide.net/node/view/217136/bgpage
====Courtship====
*Some Taeniapterinae are thought to wave their white-tipped front legs attract females.
**https://bugguide.net/node/view/217136/bgpage
*''Physiphora clausa'' appear to use leg-waving in courtship displays.
**https://www.flickr.com/photos/jean_hort/4663220062
*Waving of forelegs is included in the complex courtship behavior of ''Physiphora demandata''
**https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1439-0310.1979.tb00298.x
====Mimics for defense====
*Stilt-legged flies ''Rainieria antennaepes'' mimic ichneumonid wasps. They extend their fore-legs in front of their head, so they look like wasp antennae.
**https://thingsbiological.wordpress.com/2012/05/21/stilt-legged-flies-rainieria-antennaepes/ 
*Some hover-fly species mimic wasps by mock stinging, leg waving, or wing wagging.
**https://www.jstor.org/stable/10.1086/674612
*Wing-waving to mimic salticid spiders.
**https://www.researchgate.net/publication/27373081 https://www.researchgate.net/publication/6083895&lt;br&gt;
&lt;br&gt;

===Number of iNat records in Acalyptrate fly families===
The [[w:acalyptratae|acalyptrate fly clade]] includes the following superfamilies and families:&lt;br&gt;

* '''Carnoidea'''
** Acartophthalmidae         0
** Australimyzidae           0
** Braulidae (bee lice)         1
** Canacidae (beach flies)         3
** Carnidae (bird flies)         0
** Chloropidae (frit flies)         259
** Cryptochetidae              1
** Inbiomyiidae                0
** Milichiidae (freeloader flies) 158
&lt;br&gt;
* '''Diopsoidea'''
** Diopsidae (stalk-eyed flies)    545
** Gobryidae                   0
** Megamerinidae               0
** Nothybidae                   0
** Psilidae (rust flies)         29
** Somatiidae                   0
** Syringogastridae            0
&lt;br&gt;
* '''Ephydroidea'''
** Camillidae  0
** Campichoetidae   0
** Curtonotidae (quasimodo flies)   15
** Diastatidae 0
** Drosophilidae (vinegar and fruit flies) 312
** Ephydridae (shore flies) 117
&lt;br&gt;
* '''Lauxanioidea'''
** Celyphidae (beetle flies)  0
** Chamaemyiidae (aphid flies)  24
** Cremifaniidae  0
** Lauxaniidae (lauxaniid flies)  710
&lt;br&gt;
* '''Nerioidea'''
** Cypselosomatidae  0
** Fergusoninidae  0
** Micropezidae (stilt-legged flies)  245
** Neriidae  109
** Strongylophthalmyiidae  0
** Tanypezidae (stretched-foot flies)  0
&lt;br&gt;
* '''Opomyzoidea'''
** Agromyzidae (leaf-miner flies) 161
** Anthomyzidae  3
** Asteiidae  4
** Aulacigastridae  2
** Clusiidae (druid flies) 2
** Marginidae  0
** Neminidae 0 
** Neurochaetidae 0
** Odiniidae  0
** Opomyzidae  4
** Periscelididae  1
** Teratomyzidae  0
** Xenasteiidae  0
&lt;br&gt;
* '''Sciomyzoidea''' 
** Coelopidae (kelp flies)  51
** Conopidae (thick-headed flies)  192
** Dryomyzidae  1
** Helcomyzidae  0
** Helosciomyzidae  0
** Heterocheilidae  0
** Huttoninidae  0
** Natalimyzidae  0
** Phaeomyiidae  0
** Ropalomeridae  1
** Sciomyzidae (marsh flies)  67
** Sepsidae (black scavenger flies)  269
&lt;br&gt;
* '''Sphaeroceroidea'''
** Chyromyidae (golden flies)  19
** Heleomyzidae (heleomyzid flies)  151
** Nannodastiidae  0
** Sphaeroceridae (lesser dung flies)  48
&lt;br&gt;
* '''Tephritoidea'''
** Ctenostylidae  1
** Lonchaeidae (lance flies) 47
** Pallopteridae (flutter-wing flies)  5
** Piophilidae (cheese skipper flies) 1
** Platystomatidae (signal flies)  683
** Pyrgotidae (scarab-pursuing flies)  119
** Richardiidae  0
** Tachiniscidae  2
** Tephritidae (fruit flies)  1,759
** Ulidiidae (picture-winged flies) 165

== References ==</text>
      <sha1>pxdq9urgr7hti5cu5q4uj48dcpf4qxj</sha1>
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        <id>1669821</id>
      </contributor>
      <comment>/* South African wasp species of Tribe Oxybelini (Crabronidae) */</comment>
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= South African wasp species of Tribe Oxybelini ([[African Arthropods/Crabroninae|Crabronidae]])=
Bohart and Menke (1976)&lt;ref name BohartMenke1976&gt;Bohart, R.M. &amp; Menke, A. S. 1976. Sphecid Wasps of the World: a Generic Revision. University of California Press, Berkeley, California. pp. 359-370 https://archive.org/details/bub_gb_FExMjuRhjpIC/page/n359/mode/2up&lt;/ref&gt; reviewed the tribe, as did Antropov (1999-2007).
== Genus Belarnoldus Antropov, 2007&lt;ref name=Antropov2007&gt;https://link.springer.com/article/10.1134/S0013873807040045&lt;/ref&gt;  ==

Belarnoldus crassus Arnold, 1936 (South Africa)

== Genus Belokohlus Antropov, 2007 ==

Belokohlus ferrieri (Kohl, 1924) (South Africa)

== Genus Belomicrinus Antropov, 2000 ==

Belomicrinus luteosquamatus Antropov, 2000 (Namibia)

Belomicrinus minutissimus (Arnold, 1936) (Namibia)

== Genus Belomicroides Kohl, 1899 ==

Belomicroides arenarius Arnold, 1960 (Zimbabwe)

Belomicroides clypeatus Antropov, 2002 (South Africa)

Belomicroides erythrogaster Antropov, 2002 (Namibia)

Belomicroides marleyi Arnold, 1927 (South Africa)

Belomicroides maximiliani Antropov, 2002 (Namibia)

Belomicroides pictus Arnold, 1927 (South Africa)

Belomicroides pictus chrysoptilus Antropov, 2002 (Namibia)

Belomicroides politus Antropov, 2002 (Namibia)

Belomicroides rift Antropov, 2002 (Kenya)

Belomicroides veronicae Antropov, 2002 (Ethiopia)

Belomicroides woji Antropov, 2002 (Namibia)

== Genus Belomicrus Costa, 1867 ==

Belomicrus mirificus Kohl, 1905 (Ethiopia)

== Genus Brimocelus Arnold, 1927 ==

Brimocelus radiatus (Arnold, 1927) (South Africa)

Brimocelus roosevelti Antropov, 2000 (South Africa)

Brimocelus schwarzi Antropov, 2000 (Namibia)

== Genus Gessus Antropov, 2001 ==

Gessus capensis Antropov, 2001 (South Africa)

== Genus Minimicroides Antropov, 2000 ==

Minimicroides perexiguus Antropov, 2000 (Namibia)

== Genus Nototis Arnold, 1927 ==

Nototis bicornutus Arnold, 1927 (South Africa)

Nototis falcidens Antropov, 2007 (Namibia)

== Genus Oxybelomorpha Brauns, 1897 ==

Oxybelomorpha braunsii (Kohl, 1923) (South Africa)

Oxybelomorpha funesta (Arnold, 1929) (South Africa)

Oxybelomorpha gessi Antropov, 2005 (South Africa)

Oxybelomorpha imitans Antropov, 2005 (South Africa)

Oxybelomorpha kohlii Brauns in Kohl, 1896 (South Africa)

Oxybelomorpha nitens Antropov, 2005 (South Africa)

Oxybelomorpha pseudosordida Antropov, 2005 (Namibia)

Oxybelomorpha pulawskii Antropov, 2005 (South Africa)

Oxybelomorpha rhodesiana (Arnold, 1927) (Zimbabwe)

Oxybelomorpha rubicunda Antropov, 2005 (Namibia)

Oxybelomorpha rufiventris (Arnold, 1936) (South Africa)

Oxybelomorpha separata Antropov, 2005 (South Africa)

Oxybelomorpha sgessae Antropov, 2005 (South Africa)

Oxybelomorpha sordida (Arnold, 1927) (South Africa)

Oxybelomorpha turneri (Arnold, 1927) (South Africa)

Oxybelomorpha wojciechi Antropov, 2005 (Namibia)

== Genus Oxybelus Latreille, 1796 ==

Oxybelus acutissimus Bischoff, 1912 (Democratic Republic of Congo)

Oxybelus acutissimus propinquus Arnold, 1927 (Zimbabwe)

Oxybelus aethiopicus Cameron, 1906 (South Africa)

Oxybelus angustus de Saussure, 1892 (South Africa)

Oxybelus arnoldi Benoit, 1951 (Democratic Republic of Congo)

Oxybelus bechuanae Arnold, 1936 (Botswana)

Oxybelus bicornutus Arnold, 1929 (Namibia, South Africa)

Oxybelus braunsi Arnold, 1927 (South Africa)

Oxybelus congophilus Benoit, 1951 (Democratic Republic of Congo)

Oxybelus coniferus Arnold, 1951 (Ethiopia)

Oxybelus cristatus de Saussure, 1892 (Madagascar)

Oxybelus curviscutis Arnold, 1927 (Zimbabwe)

Oxybelus dissimilis Arnold, 1934 (Zimbabwe)

Oxybelus eburneoguttatus Arnold, 1952 (Zimbabwe)

Oxybelus flavicornis Arnold, 1927 (Zimbabwe)

Oxybelus flavicornis nyassae Arnold, 1927 (Tanzania)

Oxybelus flaviventris Arnold, 1927 (Zimbabwe)

Oxybelus fraudulentus Arnold, 1929 (Namibia)

Oxybelus harraricus Arnold, 1927 (Ethiopia)

Oxybelus hessei Arnold, 1929 (Namibia)

Oxybelus imperialis Gerstaecker, 1867 (South Africa)

Oxybelus lepturus Arnold, 1927 (Zimbabwe)

Oxybelus limatus Arnold, 1927 (Zimbabwe)

Oxybelus lingula Gerstaecker, 1867 (South Africa)

Oxybelus matabele Arnold, 1927 (Zimbabwe)

Oxybelus metopias Kohl, 1894 (Mozambique)

Oxybelus nasutus Bischoff, 1913 (Namibia)

Oxybelus natalensis Arnold, 1927 (South Africa)

Oxybelus neuvillei Magretti, 1908 (Kenya)

Oxybelus pallidus Arnold, 1927 (Ethiopia, Tanzania)

Oxybelus paucipunctatus Arnold, 1927 (Zimbabwe)

Oxybelus peringueyi de Saussure, 1892 (South Africa)

Oxybelus perornatus Arnold, 1945 (Madagascar)

Oxybelus pictus Arnold, 1927 (Zimbabwe)

Oxybelus pilosus Arnold, 1927 (Ethiopia)

Oxybelus rubrocaudatus Arnold, 1927 (Zimbabwe)

Oxybelus ruficaudis Cameron, 1905 (South Africa)

Oxybelus ruficaudis melanarius Arnold, 1927 (South Africa)

Oxybelus solitarius Arnold, 1927 (Zimbabwe)

Oxybelus stevensoni Arnold, 1927 (Zimbabwe)

Oxybelus subcristatus de Saussure, 1892 (Madagascar)

Oxybelus taschenbergi Kohl, 1875 (South Africa)

Oxybelus willowmorensis Arnold, 1927 (South Africa)

Oxybelus woosnami Arnold, 1927 (Botswana, South Africa)

Oxybelus zavattarii Guiglia, 1943 (Ethiopia)

== Genus Wojus Antropov, 1999 ==

Wojus inopinatus Antropov, 1999 (South Africa)&lt;br&gt;
&lt;br&gt;

= South African wasp species of Subtribe Gastrosericina ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus ''Gastrosericus'' ==
There are 25 Afrotropical species; four in South Africa.

== Genus ''Kohliella'' Brauns, 1910 &lt;ref&gt;http://www.biodiversitylibrary.org/page/35572001&lt;/ref&gt;==

There are three species of ''Kohliella''; two are Afrotropical.&lt;ref&gt;https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm&lt;/ref&gt; 

''Kohliella alaris'' is found in South Africa and Zimbabwe; it hunts tree crickets.&lt;ref&gt;Gess, S.K. &amp; Gess, F.W. 2014. Wasps and bees in southern Africa. SANBI Biodiversity Series 24. South African National Biodiversity Institute, Pretoria. p. 71-72. https://archive.org/details/waspsbeesinsouth24gess/page/70/mode/2up&lt;/ref&gt;

== Genus ''Parapiagetia'' ==


== Genus ''Tachytes'' ==
There are 79 Afrotropical species; 15 in South Africa.

== Genus ''Tachysphex '' ==
There are 128 Afrotropical species; 41 in South Africa.

== Genus ''Larropsis '' ==

''Larropsis (Ancistromma) obliqua'' (F. Smith); description in Arnold, 1923b:218 as ''Tachytes obliquus''
== Genus ''Tachytella '' ==
== Genus ''Prosopigastra'' ==
== Genus ''Holotachysphex '' ==
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;


= Southern African wasp species of Tribe Trypoxylini ([[African Arthropods/Crabroninae|Crabronidae]]) =

== Genus ''Pison'' Jurine, 1808 ==

Arnold ([http://www.biodiversitylibrary.org/page/60327574 1924, 1-10]) has a key and descriptions.

*''Pison allonymum'' Schulz, 1906 (South Africa; probably most of southern Africa)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance 1.5 to 2.5 times the diameter of an ocellus;
**Fairly long, whitish or silvery pilosity on head and thorax, more dense on the temples than elsewhere.&lt;ref name=Arnold1924&gt;Arnold, G. (1924) The Sphegidae of South Africa. Part V. Annals of the Transvaal Museum 11:1-4 http://www.biodiversitylibrary.org/page/60327575&lt;/ref&gt;

*''Pison atrum'' (Spinola, 1808:253) described by Cameron as ''Pison montanum'' (Kenya, South Africa, Zambia)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance not greater than the diameter of an ocellus;
**Pronotal collar longer than in ''allonymum''.

*''Pison transvaalense'' Cameron, 1910 (South Africa; probably most of southern Africa to Tanzania and Uganda)
**Head and thorax dull; finely and closely punctured;
**Distance between the posterior ocelli and the eyes is equal to a third to a half of the diameter of the ocellus.


*''Pison auratum'' Shuckard, 1838 (an Australian species; see Pulawski, 2018:85 http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Pulawski_2018.pdf)

*''Pison denticeps'' Cameron, 1910 (South Africa; &quot;Transvaal&quot;. Two cubital cells; he only record seems to be the description)

*''Pison repentinum'' Arnold, 1940 (Zimbabwe)

*''Pison rufitarse'' Arnold, 1944 (Zimbabwe)

*''Pison scruposum'' Arnold, 1955 (Zimbabwe)

== Genus ''Trypoxylon'' Latreille, 1796 ==

*''Trypoxylon abditum'' Arnold, 1924 (South Africa)

*''Trypoxylon algoense'' Arnold, 1924 (South Africa)

*''Trypoxylon arnoldi'' Menke, 1976 (South Africa, Tanzania)

*''Trypoxylon braunsi'' Arnold, 1924 (South Africa)

*''Trypoxylon capense'' Cameron, 1905 (South Africa)

*''Trypoxylon cataractae'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon chirindense'' Arnold, 1936 (Burundi, Democratic Republic of Congo, Rwanda, Uganda, Zimbabwe)

*''Trypoxylon foveatum'' Cameron, 1904 (South Africa)

*''Trypoxylon inconstans'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon infimum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon kohli'' Arnold, 1924 (South Africa)

*''Trypoxylon letiferum'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon lissonotum'' Cameron, 1910 (South Africa)

*''Trypoxylon montivagum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon nodosum'' Arnold, 1944 (Zimbabwe)

*''Trypoxylon punctatissimum'' Arnold, 1924 (South Africa)

*''Trypoxylon stevensoni'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon stroudi'' Gribodo, 1884 (Ethiopia, South Africa, Democratic Republic of Congo)

*''Trypoxylon testaceipes'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon triste'' Arnold, 1924 (Zimbabwe)

= Pompilidae of South Africa =
== South African Pompilidae with fore-wings mainly orange to yellow with fuscous (darker or blackish) wing-tips ==
&lt;gallery mode=packed heights=200&gt;
Inaturalist 258649905 b.jpg
Hemipepsis hilaris - inaturalist 10850475.jpg
Cyphononyx decipiens inat 26259647 b.jpg
Tachypompilus ignitus inaturalist 311015843 02.jpg
Pompilidae 2021 12 12 inaturalist 313386858 04.jpg
Pompilidae 2020 04 13 inaturalist 43563902 06.jpg
&lt;/gallery&gt;
*The extent of the fuscous colour can be limited to the apex of the wing beyond the cells, or extend into the cells to a varying extent.
*
&lt;br&gt;

== South African Pompilidae with fore-wings fuscous (black or very dark) ==
*The wings often have green-blue-violet reflections.
&lt;gallery mode=packed heights=200&gt;
Pompilidae 2019 05 01 2835.jpg|Female ''Batozonellus fuliginosus''
Pompilidae inaturalist 124148802 01.jpg|Female ''Cyphononyx optimus''
Pompilidae 2021 12 18 iNat 316501919 a.jpg|Female ''Cyphononyx obscurus''
Pompilidae 2025 03 14 iNat 266538336 a.jpg|Male ''Hemipepsis vindex''
Pompilidae_2019_05_28_0256.jpg|
Spider-hunting Wasp (Hemipepsis) female (12640106905).jpg|''Hemipepsis'' sp.
&lt;/gallery&gt;

&lt;br&gt;
=== Species  with black antennae, legs, head, thorax and abdomen ===
Some parts may be brown.

*''Java atropos''
*''Cyphononyx obscurus''
*''Hemipepsis vindex''
*''Hemipepsis vespertilio''
*''Hemipepsis braunsi''
*''Batozonellus fuliginosus''
&lt;br&gt;
=== Species with black antennae, head, thorax and abdomen, but legs (or parts of some legs) yellow to red ===
*''Cyphononyx optimus''
*''Paracyphononyx zonatus''
&lt;br&gt;
&lt;br&gt;

== South African Pompilidae with fore-wings mainly hyaline to fuscous-hyaline ==
&lt;gallery mode=packed heights=200&gt;
Pompilidae inaturalist 123577538.jpg
Pompilidae inaturalist 46961473.jpg
Pompilidae iN 144781033 03.jpg

&lt;/gallery&gt;
*With fuscous (darker) wing apex
*One or two fuscous bands (faciated or bifaciated)
*Hyaline parts can be clouded (whiteish clouding) or coloured (yellow-tinted)


&lt;br&gt;
== South African Ceropalinae ==
Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region: [https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 Madl, 2020]
*''Ceropales africana'' Móczar, 1989. - {{font color||yellow|''helvetica'' group}} (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales cribrata cribrata'' A. Costa, 1881; key in Móczár 1986a: 321 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales {{font color||#0f0|(Priesnerius)}} gessi'' Móczar, 1988 (South Africa)
*''Ceropales {{font color||#0f0|(Priesnerius)}} grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales karooensis'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}} (Namibia, South Africa)
*''Ceropales kriechbaumeri'' Magretti, 1884 - {{font color||yellow|''helvetica'' group}} (Burkina Faso, Nigeria, South Africa?, Uganda, Zimbabwe?)
*''Ceropales {{font color||#0f0|(Priesnerius)}} kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Senegal, South Africa, Togo, Zimbabwe) 
*''Ceropales lawrencei'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales picta'' Shuckard, 1837; key in Móczár 1986b: 125 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus'' Cameron, 1904; key in Móczár 1986a: 320 (Lesotho, South Africa)
**''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
**''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
**= Hemiceropales scobinifera (Arnold, 1937): Móczár 1986a: 319
*''Ceropales (Bifidoceropales) sulciscutis'' Cameron, 1910; key in Móczár 1990: 61 (South Africa, Tanzania)
*''Ceropales waltoni'' Arnold, 1959 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989: 12 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
&lt;br&gt;

==Afrotropical Ceropalinae ==

Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region (Madl, 2020).&lt;ref name=Madl2020&gt;Madl, M. (2020). Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region. Zeitschrift der Arbeitsgemeinschaft Österreichischer Entomologen 72: 73-84.
[https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 PDF]&lt;/ref&gt;


Ceropalinae can be defined by:&lt;ref name=Brothers1993&gt;Brothers, D. J. &amp; Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. &amp; Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143&lt;/ref&gt;&lt;ref name=Waichert2015&gt; Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., &amp; Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287. {{doi|10.1111/zoj.12272}} [https://www.researchgate.net/publication/282015793 PDF]&lt;/ref&gt;

== Genera and species of Afrotropical Ceropalinae ==

This list is based on that of [https://www.waspweb.org/Pompiloidea/Pompilidae/Ceropalinae/index.htm '''waspweb'''] with changes following the Catalogue of Life (Kroupa &amp; Schmid-Egger, 2025)&lt;ref name=CoL2025&gt; Kroupa, A. S., &amp; Schmid-Egger, C. (2025). Hymenoptera Information System, Pompilidae of the World (version 2019-09). In O. Bánki, Y. Roskov, M. Döring, G. Ower, D. R. Hernández Robles, C. A. Plata Corredor, T. Stjernegaard Jeppesen, A. Örn, T. Pape, D. Hobern, S. Garnett, H. Little, R. E. DeWalt, J. Miller, T. Orrell, R. Aalbu, J. Abbott, C. Aedo, E. Aescht, et al., Catalogue of Life (Version 2025-07-10). Catalogue of Life Foundation, Amsterdam, Netherlands. https://doi.org/10.48580/dg9ld-4kv &lt;/ref&gt; and [[w:George_Arnold_(entomologist)|papers by Arnold (1932-1962)]].&lt;br&gt;

=== Genus ''Ceropales'' ===
*''Ceropales africana'' Móczar, 1989. (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales arnoldi'' Móczar, 1988 (Namibia)
*''Ceropales atra'' Móczar, 1991 (Botswana)
*''Ceropales cribrata cribrata'' A. Costa, 1881 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales cribrata maculipes'' Móczar, 1986 (Zambia)
*''Ceropales carinitifrons'' Wahis, 1986 (Madagascar)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales dayi'' Móczar, 1989 (Kenya)
*''Ceropales ferrugo'' Móczar, 1989 (Kenya)
*''Ceropales gambiae'' Móczar, 1989 (Burkina Faso, Cameroon, Democratic Republic of Congo, Gambia, Nigeria, Senegal, Sierra Leone)
*''Ceropales gessi'' Móczar, 1988 (South Africa)
*''Ceropales grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales juncoi'' Giner Mari, 1945 (Chad, Egypt, Israel, Pakistan, Somalia, Sudan, Western Sahara)
*''Ceropales karooensis'' Arnold, 1937 (Namibia, South Africa)
*''Ceropales kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Togo, Zimbabwe)
*''Ceropales kriechbaumeri'' Magretti, 1884 (Burkina Faso, Nigeria, South Africa, Uganda, Zimbabwe)
*''Ceropales latifasciatus'' Arnold, 1937 (Ethiopia)
*''Ceropales lawrencei'' Arnold, 1937 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales levipleuris'' Wahis, 1987 (Madagascar)
*''Ceropales maliensis'' Móczar, 1989 (Mali, Senegal)
*''Ceropales maroccana'' Beaumont, 1947 (Burkina Faso, Democratic Republic of Congo, Gambia, Ghana, Ivory Coast, Nigeria, Senegal, Zimbabwe. Also Palaearctic region)
*''Ceropales multipicta'' Arnold, 1937 (Botswana, Namibia)
*''Ceropales picta'' Shuckard, 1837 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus punctulatus'' Cameron, 1904 (Lesotho, South Africa)
*''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
*''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales ruficollis'' Cameron, 1910 (Kenya, Tanzania)
*''Ceropales saegeri'' Móczar, 1988 (Democratic Reublic of Congo)
*''Ceropales senegalensis'' Móczar, 1988 (Burkina Faso, Cameroon, Senegal)
**''Ceropales senegalensis mbouri'' Móczar, 1988 (Senegal)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
*''Ceropales seyrigi'' Wahis, 1987 (Madagascar)
*''Ceropales spinolai'' Móczar, 1988 (Guinea)
*''Ceropales subhelvetica'' Móczar, 1988 (Burkina Faso, Senegal. Also Palaearctic: Israel)
*''Ceropales sulciscutis'' Cameron, 1910 (South Africa, Tanzania)
**''Ceropales sulciscutis raymondi'' Móczar, 1990 (Democratic Republic of Congo)
*''Ceropales variolosus'' Arnold, 1937 (Democratic Republic of Congo, Ghana, Guinea, Mali, Nigeria, Senegal, Sudan, Togo, Uganda)
*''Ceropales waltoni'' Arnold, 1959 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
*''Ceropales yemeni'' Móczar, 1988 (Yemen. Also Palaearctic: Israel, Saudi Arabia)
&lt;br&gt;
=== Genus ''Irenangelus'' ===
*''Irenangelus madescassus'' Wahis, 1988 (Madagascar)
&lt;br&gt;

==Eumeninae==
Photos of ''Antodynerus'' on GBIF:&lt;br&gt;
''alboniger'': https://www.gbif.org/occurrence/1248689053 (CC BY-NC-SA 3.0)&lt;br&gt; 
''hova'': https://www.gbif.org/occurrence/1320165802 (CC0 1.0)&lt;br&gt;
''kelneri'': https://www.gbif.org/occurrence/3762658306 (CC BY-NC-SA 4.0)&lt;br&gt; 
''lugubris'': https://www.gbif.org/occurrence/1248689125 (CC BY-NC-SA 3.0)&lt;br&gt; 
''seyrigi'': https://www.gbif.org/occurrence/1322648015 (CC0 1.0)&lt;br&gt;
''sheffieldi'': https://www.gbif.org/occurrence/1318932924 (CC0 1.0)&lt;br&gt;
''silaos'': https://www.gbif.org/occurrence/1320574593 (CC0 1.0)&lt;br&gt;

==Ants==
'''Subfamilies of Formicidae (WaspWeb)'''

Number of iNaturalist records for subfamilies of Formicidae in Africa (2023-05-23)
Amblyoponinae              7
Dolichoderinae           630
Dorylinae                 1 167
Formicinae            10 396       Camponotus   6 090; Lepisiota 1 046
Myrmicinae              8 484       Crematogaster  1 786;   Pheidole  1 468;   Messor  1 156 
Ponerinae                1 623
Proceratiinae                  3
Pseudomyrmecinae   296


Aenictinae One Afrotropical genus ''Aenictus'' &lt;br&gt;

Aenictogitoninae One Afrotropical genus ''Aenictogiton'' &lt;br&gt;

Amblyoponinae Five Afrotropical genera &lt;br&gt;

Apomyrminae One Afrotropical genus ''Apomyrma'' &lt;br&gt; 

Cerapachyinae Five Afrotropical genera&lt;br&gt;

Dolichoderinae Eight Afrotropical genera&lt;br&gt;

Dorylinae One Afrotropical genus ''Dorylus'' &lt;br&gt;

Formicinae 20 Afrotropical genera&lt;br&gt;

Leptanillinae One Afrotropical genus ''Leptanilla'' &lt;br&gt;

Myrmicinae 37 Afrotropical genera &lt;br&gt;

Ponerinae 18 Afrotropical genera &lt;br&gt;

Proceratiinae Three Afrotropical genera  &lt;br&gt;

Pseudomyrmecinae One Afrotropical genus Tetraponera &lt;br&gt;


&lt;gallery mode=packed heights=200&gt;
Aenictogiton sp.jpg|''Aenictogiton'' sp., Aenictogitoninae 
Apomyrma stygia casent0101444 profile 1.jpg|''Apomyrma stygia'', Apomyrminae 
Cerapachys coxalis casent0173076 profile 1.jpg|''Cerapachys coxalis'', Cerapachyinae 
Cerapachys centurio castype12081-02 profile 1.jpg|''Cerapachys centurio'', Cerapachyinae
Tapinoma subtile casent0132840 dorsal 1.jpg|''Tapinoma subtile'', Dolichoderinae 
Dorylus helvolus, a, Seringveld.jpg|''Dorylus helvolus'', Dorylinae  
Polyrhachis schistacea00.jpg|''Polyrhachis schistacea'', Formicinae 
Anoplolepis custodiens, met prooi, a, Krugersdorp.jpg|''Anoplolepis custodiens'', Formicinae 
AFRICAN THIEF ANT SIX.jpg|''Carebara vidua'', Myrmicinae 
Millipede Hunter Ant (Plectroctena mandibularis) (11904420373).jpg|''Plectroctena mandibularis'', Ponerinae 
Discothyrea hewitti sam-hym-c000061a profile 1.jpg|''Discothyrea hewitti'', Proceratiinae 
Probolomyrmex filiformis casent0102141 profile 1.jpg|''Probolomyrmex filiformis'', Proceratiinae 
Slender Ant (Tetraponera natalensis) (30538051244).jpg|''Tetraponera natalensis'', Pseudomyrmecinae
&lt;/gallery&gt;

== N-P interactions ==
Dai, Z., Liu, G., Chen, H., Chen, C., Wang, J., Ai, S., Wei, D., Li, D., Ma, B., Tang, C., Brookes, P.C. and Xu, J., 2020. Long-term nutrient inputs shift soil microbial functional profiles of phosphorus cycling in diverse agroecosystems. The ISME journal, 14(3), pp.757-770.
'''Abstract'''
Microorganisms play an important role in soil phosphorus (P) cycling and regulation of P availability in agroecosystems. However, the responses of the functional and ecological traits of P-transformation microorganisms to long-term nutrient inputs are largely unknown. This study used metagenomics to investigate changes in the relative abundance of microbial P-transformation genes at four long-term experimental sites that received various inputs of N and P nutrients (up to 39 years). Long-term P input increased microbial P immobilization by decreasing the relative abundance of the P-starvation response gene (phoR) and increasing that of the low-affinity inorganic phosphate transporter gene (pit). This contrasts with previous findings that low-P conditions facilitate P immobilization in culturable microorganisms in short-term studies. In comparison, long-term nitrogen (N) input significantly decreased soil pH, and consequently decreased the relative abundances of total microbial P-solubilizing genes and the abundances of Actinobacteria, Gammaproteobacteria, and Alphaproteobacteria containing genes coding for alkaline phosphatase, and weakened the connection of relevant key genes. This challenges the concept that microbial P-solubilization capacity is mainly regulated by N:P stoichiometry. It is concluded that long-term N inputs decreased microbial P-solubilizing and mineralizing capacity while P inputs favored microbial immobilization via altering the microbial functional profiles, providing a novel insight into the regulation of P cycling in sustainable agroecosystems from a microbial perspective.

==Diptera==
===Wing and leg-waving behavior in flies===
====Food detection====
*''Rhagio lineola'' and ''R. tringarius'' feed on pollen and/or honeydew, which they locate by sweeping their front legs across the surface of leaves. They have a few fine hairs on their front legs, probably for this purpose. Other Rhagionidae do not have these hairs. 
**https://www.researchgate.net/publication/359760392
*It is also possible that some flies sample the air with the chemical sensors on their legs or feet.
**https://bugguide.net/node/view/217136/bgpage
====Courtship====
*Some Taeniapterinae are thought to wave their white-tipped front legs attract females.
**https://bugguide.net/node/view/217136/bgpage
*''Physiphora clausa'' appear to use leg-waving in courtship displays.
**https://www.flickr.com/photos/jean_hort/4663220062
*Waving of forelegs is included in the complex courtship behavior of ''Physiphora demandata''
**https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1439-0310.1979.tb00298.x
====Mimics for defense====
*Stilt-legged flies ''Rainieria antennaepes'' mimic ichneumonid wasps. They extend their fore-legs in front of their head, so they look like wasp antennae.
**https://thingsbiological.wordpress.com/2012/05/21/stilt-legged-flies-rainieria-antennaepes/ 
*Some hover-fly species mimic wasps by mock stinging, leg waving, or wing wagging.
**https://www.jstor.org/stable/10.1086/674612
*Wing-waving to mimic salticid spiders.
**https://www.researchgate.net/publication/27373081 https://www.researchgate.net/publication/6083895&lt;br&gt;
&lt;br&gt;

===Number of iNat records in Acalyptrate fly families===
The [[w:acalyptratae|acalyptrate fly clade]] includes the following superfamilies and families:&lt;br&gt;

* '''Carnoidea'''
** Acartophthalmidae         0
** Australimyzidae           0
** Braulidae (bee lice)         1
** Canacidae (beach flies)         3
** Carnidae (bird flies)         0
** Chloropidae (frit flies)         259
** Cryptochetidae              1
** Inbiomyiidae                0
** Milichiidae (freeloader flies) 158
&lt;br&gt;
* '''Diopsoidea'''
** Diopsidae (stalk-eyed flies)    545
** Gobryidae                   0
** Megamerinidae               0
** Nothybidae                   0
** Psilidae (rust flies)         29
** Somatiidae                   0
** Syringogastridae            0
&lt;br&gt;
* '''Ephydroidea'''
** Camillidae  0
** Campichoetidae   0
** Curtonotidae (quasimodo flies)   15
** Diastatidae 0
** Drosophilidae (vinegar and fruit flies) 312
** Ephydridae (shore flies) 117
&lt;br&gt;
* '''Lauxanioidea'''
** Celyphidae (beetle flies)  0
** Chamaemyiidae (aphid flies)  24
** Cremifaniidae  0
** Lauxaniidae (lauxaniid flies)  710
&lt;br&gt;
* '''Nerioidea'''
** Cypselosomatidae  0
** Fergusoninidae  0
** Micropezidae (stilt-legged flies)  245
** Neriidae  109
** Strongylophthalmyiidae  0
** Tanypezidae (stretched-foot flies)  0
&lt;br&gt;
* '''Opomyzoidea'''
** Agromyzidae (leaf-miner flies) 161
** Anthomyzidae  3
** Asteiidae  4
** Aulacigastridae  2
** Clusiidae (druid flies) 2
** Marginidae  0
** Neminidae 0 
** Neurochaetidae 0
** Odiniidae  0
** Opomyzidae  4
** Periscelididae  1
** Teratomyzidae  0
** Xenasteiidae  0
&lt;br&gt;
* '''Sciomyzoidea''' 
** Coelopidae (kelp flies)  51
** Conopidae (thick-headed flies)  192
** Dryomyzidae  1
** Helcomyzidae  0
** Helosciomyzidae  0
** Heterocheilidae  0
** Huttoninidae  0
** Natalimyzidae  0
** Phaeomyiidae  0
** Ropalomeridae  1
** Sciomyzidae (marsh flies)  67
** Sepsidae (black scavenger flies)  269
&lt;br&gt;
* '''Sphaeroceroidea'''
** Chyromyidae (golden flies)  19
** Heleomyzidae (heleomyzid flies)  151
** Nannodastiidae  0
** Sphaeroceridae (lesser dung flies)  48
&lt;br&gt;
* '''Tephritoidea'''
** Ctenostylidae  1
** Lonchaeidae (lance flies) 47
** Pallopteridae (flutter-wing flies)  5
** Piophilidae (cheese skipper flies) 1
** Platystomatidae (signal flies)  683
** Pyrgotidae (scarab-pursuing flies)  119
** Richardiidae  0
** Tachiniscidae  2
** Tephritidae (fruit flies)  1,759
** Ulidiidae (picture-winged flies) 165

== References ==</text>
      <sha1>77m1lu9adkfto688qlh94gq2wp94ujb</sha1>
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= South African wasp species of Tribe Oxybelini ([[African Arthropods/Crabroninae|Crabronidae]])=
Bohart and Menke (1976)&lt;ref name BohartMenke1976&gt;Bohart, R.M. &amp; Menke, A. S. 1976. Sphecid Wasps of the World: a Generic Revision. University of California Press, Berkeley, California. pp. 359-370 https://archive.org/details/bub_gb_FExMjuRhjpIC/page/n359/mode/2up&lt;/ref&gt; reviewed the tribe, as did Antropov (1999-2007).
== Genus Belarnoldus Antropov, 2007&lt;ref name=Antropov2007&gt;Antropov, A. V. (2007). On the taxonomy of South African digger wasps of the tribe Oxybelini (Hymenoptera, Crabronidae). Entomological Review, 87(4), 413-430. https://link.springer.com/article/10.1134/S0013873807040045&lt;/ref&gt;  ==

Belarnoldus crassus Arnold, 1936 (South Africa)

== Genus Belokohlus Antropov, 2007 ==

Belokohlus ferrieri (Kohl, 1924) (South Africa)

== Genus Belomicrinus Antropov, 2000 ==

Belomicrinus luteosquamatus Antropov, 2000 (Namibia)

Belomicrinus minutissimus (Arnold, 1936) (Namibia)

== Genus Belomicroides Kohl, 1899 ==

Belomicroides arenarius Arnold, 1960 (Zimbabwe)

Belomicroides clypeatus Antropov, 2002 (South Africa)

Belomicroides erythrogaster Antropov, 2002 (Namibia)

Belomicroides marleyi Arnold, 1927 (South Africa)

Belomicroides maximiliani Antropov, 2002 (Namibia)

Belomicroides pictus Arnold, 1927 (South Africa)

Belomicroides pictus chrysoptilus Antropov, 2002 (Namibia)

Belomicroides politus Antropov, 2002 (Namibia)

Belomicroides rift Antropov, 2002 (Kenya)

Belomicroides veronicae Antropov, 2002 (Ethiopia)

Belomicroides woji Antropov, 2002 (Namibia)

== Genus Belomicrus Costa, 1867 ==

Belomicrus mirificus Kohl, 1905 (Ethiopia)

== Genus Brimocelus Arnold, 1927 ==

Brimocelus radiatus (Arnold, 1927) (South Africa)

Brimocelus roosevelti Antropov, 2000 (South Africa)

Brimocelus schwarzi Antropov, 2000 (Namibia)

== Genus Gessus Antropov, 2001 ==

Gessus capensis Antropov, 2001 (South Africa)

== Genus Minimicroides Antropov, 2000 ==

Minimicroides perexiguus Antropov, 2000 (Namibia)

== Genus Nototis Arnold, 1927 ==

Nototis bicornutus Arnold, 1927 (South Africa)

Nototis falcidens Antropov, 2007 (Namibia)

== Genus Oxybelomorpha Brauns, 1897 ==

Oxybelomorpha braunsii (Kohl, 1923) (South Africa)

Oxybelomorpha funesta (Arnold, 1929) (South Africa)

Oxybelomorpha gessi Antropov, 2005 (South Africa)

Oxybelomorpha imitans Antropov, 2005 (South Africa)

Oxybelomorpha kohlii Brauns in Kohl, 1896 (South Africa)

Oxybelomorpha nitens Antropov, 2005 (South Africa)

Oxybelomorpha pseudosordida Antropov, 2005 (Namibia)

Oxybelomorpha pulawskii Antropov, 2005 (South Africa)

Oxybelomorpha rhodesiana (Arnold, 1927) (Zimbabwe)

Oxybelomorpha rubicunda Antropov, 2005 (Namibia)

Oxybelomorpha rufiventris (Arnold, 1936) (South Africa)

Oxybelomorpha separata Antropov, 2005 (South Africa)

Oxybelomorpha sgessae Antropov, 2005 (South Africa)

Oxybelomorpha sordida (Arnold, 1927) (South Africa)

Oxybelomorpha turneri (Arnold, 1927) (South Africa)

Oxybelomorpha wojciechi Antropov, 2005 (Namibia)

== Genus Oxybelus Latreille, 1796 ==

Oxybelus acutissimus Bischoff, 1912 (Democratic Republic of Congo)

Oxybelus acutissimus propinquus Arnold, 1927 (Zimbabwe)

Oxybelus aethiopicus Cameron, 1906 (South Africa)

Oxybelus angustus de Saussure, 1892 (South Africa)

Oxybelus arnoldi Benoit, 1951 (Democratic Republic of Congo)

Oxybelus bechuanae Arnold, 1936 (Botswana)

Oxybelus bicornutus Arnold, 1929 (Namibia, South Africa)

Oxybelus braunsi Arnold, 1927 (South Africa)

Oxybelus congophilus Benoit, 1951 (Democratic Republic of Congo)

Oxybelus coniferus Arnold, 1951 (Ethiopia)

Oxybelus cristatus de Saussure, 1892 (Madagascar)

Oxybelus curviscutis Arnold, 1927 (Zimbabwe)

Oxybelus dissimilis Arnold, 1934 (Zimbabwe)

Oxybelus eburneoguttatus Arnold, 1952 (Zimbabwe)

Oxybelus flavicornis Arnold, 1927 (Zimbabwe)

Oxybelus flavicornis nyassae Arnold, 1927 (Tanzania)

Oxybelus flaviventris Arnold, 1927 (Zimbabwe)

Oxybelus fraudulentus Arnold, 1929 (Namibia)

Oxybelus harraricus Arnold, 1927 (Ethiopia)

Oxybelus hessei Arnold, 1929 (Namibia)

Oxybelus imperialis Gerstaecker, 1867 (South Africa)

Oxybelus lepturus Arnold, 1927 (Zimbabwe)

Oxybelus limatus Arnold, 1927 (Zimbabwe)

Oxybelus lingula Gerstaecker, 1867 (South Africa)

Oxybelus matabele Arnold, 1927 (Zimbabwe)

Oxybelus metopias Kohl, 1894 (Mozambique)

Oxybelus nasutus Bischoff, 1913 (Namibia)

Oxybelus natalensis Arnold, 1927 (South Africa)

Oxybelus neuvillei Magretti, 1908 (Kenya)

Oxybelus pallidus Arnold, 1927 (Ethiopia, Tanzania)

Oxybelus paucipunctatus Arnold, 1927 (Zimbabwe)

Oxybelus peringueyi de Saussure, 1892 (South Africa)

Oxybelus perornatus Arnold, 1945 (Madagascar)

Oxybelus pictus Arnold, 1927 (Zimbabwe)

Oxybelus pilosus Arnold, 1927 (Ethiopia)

Oxybelus rubrocaudatus Arnold, 1927 (Zimbabwe)

Oxybelus ruficaudis Cameron, 1905 (South Africa)

Oxybelus ruficaudis melanarius Arnold, 1927 (South Africa)

Oxybelus solitarius Arnold, 1927 (Zimbabwe)

Oxybelus stevensoni Arnold, 1927 (Zimbabwe)

Oxybelus subcristatus de Saussure, 1892 (Madagascar)

Oxybelus taschenbergi Kohl, 1875 (South Africa)

Oxybelus willowmorensis Arnold, 1927 (South Africa)

Oxybelus woosnami Arnold, 1927 (Botswana, South Africa)

Oxybelus zavattarii Guiglia, 1943 (Ethiopia)

== Genus Wojus Antropov, 1999 ==

Wojus inopinatus Antropov, 1999 (South Africa)&lt;br&gt;
&lt;br&gt;

= South African wasp species of Subtribe Gastrosericina ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus ''Gastrosericus'' ==
There are 25 Afrotropical species; four in South Africa.

== Genus ''Kohliella'' Brauns, 1910 &lt;ref&gt;http://www.biodiversitylibrary.org/page/35572001&lt;/ref&gt;==

There are three species of ''Kohliella''; two are Afrotropical.&lt;ref&gt;https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm&lt;/ref&gt; 

''Kohliella alaris'' is found in South Africa and Zimbabwe; it hunts tree crickets.&lt;ref&gt;Gess, S.K. &amp; Gess, F.W. 2014. Wasps and bees in southern Africa. SANBI Biodiversity Series 24. South African National Biodiversity Institute, Pretoria. p. 71-72. https://archive.org/details/waspsbeesinsouth24gess/page/70/mode/2up&lt;/ref&gt;

== Genus ''Parapiagetia'' ==


== Genus ''Tachytes'' ==
There are 79 Afrotropical species; 15 in South Africa.

== Genus ''Tachysphex '' ==
There are 128 Afrotropical species; 41 in South Africa.

== Genus ''Larropsis '' ==

''Larropsis (Ancistromma) obliqua'' (F. Smith); description in Arnold, 1923b:218 as ''Tachytes obliquus''
== Genus ''Tachytella '' ==
== Genus ''Prosopigastra'' ==
== Genus ''Holotachysphex '' ==
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;


= Southern African wasp species of Tribe Trypoxylini ([[African Arthropods/Crabroninae|Crabronidae]]) =

== Genus ''Pison'' Jurine, 1808 ==

Arnold ([http://www.biodiversitylibrary.org/page/60327574 1924, 1-10]) has a key and descriptions.

*''Pison allonymum'' Schulz, 1906 (South Africa; probably most of southern Africa)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance 1.5 to 2.5 times the diameter of an ocellus;
**Fairly long, whitish or silvery pilosity on head and thorax, more dense on the temples than elsewhere.&lt;ref name=Arnold1924&gt;Arnold, G. (1924) The Sphegidae of South Africa. Part V. Annals of the Transvaal Museum 11:1-4 http://www.biodiversitylibrary.org/page/60327575&lt;/ref&gt;

*''Pison atrum'' (Spinola, 1808:253) described by Cameron as ''Pison montanum'' (Kenya, South Africa, Zambia)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance not greater than the diameter of an ocellus;
**Pronotal collar longer than in ''allonymum''.

*''Pison transvaalense'' Cameron, 1910 (South Africa; probably most of southern Africa to Tanzania and Uganda)
**Head and thorax dull; finely and closely punctured;
**Distance between the posterior ocelli and the eyes is equal to a third to a half of the diameter of the ocellus.


*''Pison auratum'' Shuckard, 1838 (an Australian species; see Pulawski, 2018:85 http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Pulawski_2018.pdf)

*''Pison denticeps'' Cameron, 1910 (South Africa; &quot;Transvaal&quot;. Two cubital cells; he only record seems to be the description)

*''Pison repentinum'' Arnold, 1940 (Zimbabwe)

*''Pison rufitarse'' Arnold, 1944 (Zimbabwe)

*''Pison scruposum'' Arnold, 1955 (Zimbabwe)

== Genus ''Trypoxylon'' Latreille, 1796 ==

*''Trypoxylon abditum'' Arnold, 1924 (South Africa)

*''Trypoxylon algoense'' Arnold, 1924 (South Africa)

*''Trypoxylon arnoldi'' Menke, 1976 (South Africa, Tanzania)

*''Trypoxylon braunsi'' Arnold, 1924 (South Africa)

*''Trypoxylon capense'' Cameron, 1905 (South Africa)

*''Trypoxylon cataractae'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon chirindense'' Arnold, 1936 (Burundi, Democratic Republic of Congo, Rwanda, Uganda, Zimbabwe)

*''Trypoxylon foveatum'' Cameron, 1904 (South Africa)

*''Trypoxylon inconstans'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon infimum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon kohli'' Arnold, 1924 (South Africa)

*''Trypoxylon letiferum'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon lissonotum'' Cameron, 1910 (South Africa)

*''Trypoxylon montivagum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon nodosum'' Arnold, 1944 (Zimbabwe)

*''Trypoxylon punctatissimum'' Arnold, 1924 (South Africa)

*''Trypoxylon stevensoni'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon stroudi'' Gribodo, 1884 (Ethiopia, South Africa, Democratic Republic of Congo)

*''Trypoxylon testaceipes'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon triste'' Arnold, 1924 (Zimbabwe)

= Pompilidae of South Africa =
== South African Pompilidae with fore-wings mainly orange to yellow with fuscous (darker or blackish) wing-tips ==
&lt;gallery mode=packed heights=200&gt;
Inaturalist 258649905 b.jpg
Hemipepsis hilaris - inaturalist 10850475.jpg
Cyphononyx decipiens inat 26259647 b.jpg
Tachypompilus ignitus inaturalist 311015843 02.jpg
Pompilidae 2021 12 12 inaturalist 313386858 04.jpg
Pompilidae 2020 04 13 inaturalist 43563902 06.jpg
&lt;/gallery&gt;
*The extent of the fuscous colour can be limited to the apex of the wing beyond the cells, or extend into the cells to a varying extent.
*
&lt;br&gt;

== South African Pompilidae with fore-wings fuscous (black or very dark) ==
*The wings often have green-blue-violet reflections.
&lt;gallery mode=packed heights=200&gt;
Pompilidae 2019 05 01 2835.jpg|Female ''Batozonellus fuliginosus''
Pompilidae inaturalist 124148802 01.jpg|Female ''Cyphononyx optimus''
Pompilidae 2021 12 18 iNat 316501919 a.jpg|Female ''Cyphononyx obscurus''
Pompilidae 2025 03 14 iNat 266538336 a.jpg|Male ''Hemipepsis vindex''
Pompilidae_2019_05_28_0256.jpg|
Spider-hunting Wasp (Hemipepsis) female (12640106905).jpg|''Hemipepsis'' sp.
&lt;/gallery&gt;

&lt;br&gt;
=== Species  with black antennae, legs, head, thorax and abdomen ===
Some parts may be brown.

*''Java atropos''
*''Cyphononyx obscurus''
*''Hemipepsis vindex''
*''Hemipepsis vespertilio''
*''Hemipepsis braunsi''
*''Batozonellus fuliginosus''
&lt;br&gt;
=== Species with black antennae, head, thorax and abdomen, but legs (or parts of some legs) yellow to red ===
*''Cyphononyx optimus''
*''Paracyphononyx zonatus''
&lt;br&gt;
&lt;br&gt;

== South African Pompilidae with fore-wings mainly hyaline to fuscous-hyaline ==
&lt;gallery mode=packed heights=200&gt;
Pompilidae inaturalist 123577538.jpg
Pompilidae inaturalist 46961473.jpg
Pompilidae iN 144781033 03.jpg

&lt;/gallery&gt;
*With fuscous (darker) wing apex
*One or two fuscous bands (faciated or bifaciated)
*Hyaline parts can be clouded (whiteish clouding) or coloured (yellow-tinted)


&lt;br&gt;
== South African Ceropalinae ==
Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region: [https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 Madl, 2020]
*''Ceropales africana'' Móczar, 1989. - {{font color||yellow|''helvetica'' group}} (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales cribrata cribrata'' A. Costa, 1881; key in Móczár 1986a: 321 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales {{font color||#0f0|(Priesnerius)}} gessi'' Móczar, 1988 (South Africa)
*''Ceropales {{font color||#0f0|(Priesnerius)}} grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales karooensis'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}} (Namibia, South Africa)
*''Ceropales kriechbaumeri'' Magretti, 1884 - {{font color||yellow|''helvetica'' group}} (Burkina Faso, Nigeria, South Africa?, Uganda, Zimbabwe?)
*''Ceropales {{font color||#0f0|(Priesnerius)}} kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Senegal, South Africa, Togo, Zimbabwe) 
*''Ceropales lawrencei'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales picta'' Shuckard, 1837; key in Móczár 1986b: 125 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus'' Cameron, 1904; key in Móczár 1986a: 320 (Lesotho, South Africa)
**''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
**''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
**= Hemiceropales scobinifera (Arnold, 1937): Móczár 1986a: 319
*''Ceropales (Bifidoceropales) sulciscutis'' Cameron, 1910; key in Móczár 1990: 61 (South Africa, Tanzania)
*''Ceropales waltoni'' Arnold, 1959 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989: 12 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
&lt;br&gt;

==Afrotropical Ceropalinae ==

Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region (Madl, 2020).&lt;ref name=Madl2020&gt;Madl, M. (2020). Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region. Zeitschrift der Arbeitsgemeinschaft Österreichischer Entomologen 72: 73-84.
[https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 PDF]&lt;/ref&gt;


Ceropalinae can be defined by:&lt;ref name=Brothers1993&gt;Brothers, D. J. &amp; Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. &amp; Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143&lt;/ref&gt;&lt;ref name=Waichert2015&gt; Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., &amp; Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287. {{doi|10.1111/zoj.12272}} [https://www.researchgate.net/publication/282015793 PDF]&lt;/ref&gt;

== Genera and species of Afrotropical Ceropalinae ==

This list is based on that of [https://www.waspweb.org/Pompiloidea/Pompilidae/Ceropalinae/index.htm '''waspweb'''] with changes following the Catalogue of Life (Kroupa &amp; Schmid-Egger, 2025)&lt;ref name=CoL2025&gt; Kroupa, A. S., &amp; Schmid-Egger, C. (2025). Hymenoptera Information System, Pompilidae of the World (version 2019-09). In O. Bánki, Y. Roskov, M. Döring, G. Ower, D. R. Hernández Robles, C. A. Plata Corredor, T. Stjernegaard Jeppesen, A. Örn, T. Pape, D. Hobern, S. Garnett, H. Little, R. E. DeWalt, J. Miller, T. Orrell, R. Aalbu, J. Abbott, C. Aedo, E. Aescht, et al., Catalogue of Life (Version 2025-07-10). Catalogue of Life Foundation, Amsterdam, Netherlands. https://doi.org/10.48580/dg9ld-4kv &lt;/ref&gt; and [[w:George_Arnold_(entomologist)|papers by Arnold (1932-1962)]].&lt;br&gt;

=== Genus ''Ceropales'' ===
*''Ceropales africana'' Móczar, 1989. (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales arnoldi'' Móczar, 1988 (Namibia)
*''Ceropales atra'' Móczar, 1991 (Botswana)
*''Ceropales cribrata cribrata'' A. Costa, 1881 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales cribrata maculipes'' Móczar, 1986 (Zambia)
*''Ceropales carinitifrons'' Wahis, 1986 (Madagascar)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales dayi'' Móczar, 1989 (Kenya)
*''Ceropales ferrugo'' Móczar, 1989 (Kenya)
*''Ceropales gambiae'' Móczar, 1989 (Burkina Faso, Cameroon, Democratic Republic of Congo, Gambia, Nigeria, Senegal, Sierra Leone)
*''Ceropales gessi'' Móczar, 1988 (South Africa)
*''Ceropales grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales juncoi'' Giner Mari, 1945 (Chad, Egypt, Israel, Pakistan, Somalia, Sudan, Western Sahara)
*''Ceropales karooensis'' Arnold, 1937 (Namibia, South Africa)
*''Ceropales kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Togo, Zimbabwe)
*''Ceropales kriechbaumeri'' Magretti, 1884 (Burkina Faso, Nigeria, South Africa, Uganda, Zimbabwe)
*''Ceropales latifasciatus'' Arnold, 1937 (Ethiopia)
*''Ceropales lawrencei'' Arnold, 1937 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales levipleuris'' Wahis, 1987 (Madagascar)
*''Ceropales maliensis'' Móczar, 1989 (Mali, Senegal)
*''Ceropales maroccana'' Beaumont, 1947 (Burkina Faso, Democratic Republic of Congo, Gambia, Ghana, Ivory Coast, Nigeria, Senegal, Zimbabwe. Also Palaearctic region)
*''Ceropales multipicta'' Arnold, 1937 (Botswana, Namibia)
*''Ceropales picta'' Shuckard, 1837 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus punctulatus'' Cameron, 1904 (Lesotho, South Africa)
*''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
*''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales ruficollis'' Cameron, 1910 (Kenya, Tanzania)
*''Ceropales saegeri'' Móczar, 1988 (Democratic Reublic of Congo)
*''Ceropales senegalensis'' Móczar, 1988 (Burkina Faso, Cameroon, Senegal)
**''Ceropales senegalensis mbouri'' Móczar, 1988 (Senegal)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
*''Ceropales seyrigi'' Wahis, 1987 (Madagascar)
*''Ceropales spinolai'' Móczar, 1988 (Guinea)
*''Ceropales subhelvetica'' Móczar, 1988 (Burkina Faso, Senegal. Also Palaearctic: Israel)
*''Ceropales sulciscutis'' Cameron, 1910 (South Africa, Tanzania)
**''Ceropales sulciscutis raymondi'' Móczar, 1990 (Democratic Republic of Congo)
*''Ceropales variolosus'' Arnold, 1937 (Democratic Republic of Congo, Ghana, Guinea, Mali, Nigeria, Senegal, Sudan, Togo, Uganda)
*''Ceropales waltoni'' Arnold, 1959 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
*''Ceropales yemeni'' Móczar, 1988 (Yemen. Also Palaearctic: Israel, Saudi Arabia)
&lt;br&gt;
=== Genus ''Irenangelus'' ===
*''Irenangelus madescassus'' Wahis, 1988 (Madagascar)
&lt;br&gt;

==Eumeninae==
Photos of ''Antodynerus'' on GBIF:&lt;br&gt;
''alboniger'': https://www.gbif.org/occurrence/1248689053 (CC BY-NC-SA 3.0)&lt;br&gt; 
''hova'': https://www.gbif.org/occurrence/1320165802 (CC0 1.0)&lt;br&gt;
''kelneri'': https://www.gbif.org/occurrence/3762658306 (CC BY-NC-SA 4.0)&lt;br&gt; 
''lugubris'': https://www.gbif.org/occurrence/1248689125 (CC BY-NC-SA 3.0)&lt;br&gt; 
''seyrigi'': https://www.gbif.org/occurrence/1322648015 (CC0 1.0)&lt;br&gt;
''sheffieldi'': https://www.gbif.org/occurrence/1318932924 (CC0 1.0)&lt;br&gt;
''silaos'': https://www.gbif.org/occurrence/1320574593 (CC0 1.0)&lt;br&gt;

==Ants==
'''Subfamilies of Formicidae (WaspWeb)'''

Number of iNaturalist records for subfamilies of Formicidae in Africa (2023-05-23)
Amblyoponinae              7
Dolichoderinae           630
Dorylinae                 1 167
Formicinae            10 396       Camponotus   6 090; Lepisiota 1 046
Myrmicinae              8 484       Crematogaster  1 786;   Pheidole  1 468;   Messor  1 156 
Ponerinae                1 623
Proceratiinae                  3
Pseudomyrmecinae   296


Aenictinae One Afrotropical genus ''Aenictus'' &lt;br&gt;

Aenictogitoninae One Afrotropical genus ''Aenictogiton'' &lt;br&gt;

Amblyoponinae Five Afrotropical genera &lt;br&gt;

Apomyrminae One Afrotropical genus ''Apomyrma'' &lt;br&gt; 

Cerapachyinae Five Afrotropical genera&lt;br&gt;

Dolichoderinae Eight Afrotropical genera&lt;br&gt;

Dorylinae One Afrotropical genus ''Dorylus'' &lt;br&gt;

Formicinae 20 Afrotropical genera&lt;br&gt;

Leptanillinae One Afrotropical genus ''Leptanilla'' &lt;br&gt;

Myrmicinae 37 Afrotropical genera &lt;br&gt;

Ponerinae 18 Afrotropical genera &lt;br&gt;

Proceratiinae Three Afrotropical genera  &lt;br&gt;

Pseudomyrmecinae One Afrotropical genus Tetraponera &lt;br&gt;


&lt;gallery mode=packed heights=200&gt;
Aenictogiton sp.jpg|''Aenictogiton'' sp., Aenictogitoninae 
Apomyrma stygia casent0101444 profile 1.jpg|''Apomyrma stygia'', Apomyrminae 
Cerapachys coxalis casent0173076 profile 1.jpg|''Cerapachys coxalis'', Cerapachyinae 
Cerapachys centurio castype12081-02 profile 1.jpg|''Cerapachys centurio'', Cerapachyinae
Tapinoma subtile casent0132840 dorsal 1.jpg|''Tapinoma subtile'', Dolichoderinae 
Dorylus helvolus, a, Seringveld.jpg|''Dorylus helvolus'', Dorylinae  
Polyrhachis schistacea00.jpg|''Polyrhachis schistacea'', Formicinae 
Anoplolepis custodiens, met prooi, a, Krugersdorp.jpg|''Anoplolepis custodiens'', Formicinae 
AFRICAN THIEF ANT SIX.jpg|''Carebara vidua'', Myrmicinae 
Millipede Hunter Ant (Plectroctena mandibularis) (11904420373).jpg|''Plectroctena mandibularis'', Ponerinae 
Discothyrea hewitti sam-hym-c000061a profile 1.jpg|''Discothyrea hewitti'', Proceratiinae 
Probolomyrmex filiformis casent0102141 profile 1.jpg|''Probolomyrmex filiformis'', Proceratiinae 
Slender Ant (Tetraponera natalensis) (30538051244).jpg|''Tetraponera natalensis'', Pseudomyrmecinae
&lt;/gallery&gt;

== N-P interactions ==
Dai, Z., Liu, G., Chen, H., Chen, C., Wang, J., Ai, S., Wei, D., Li, D., Ma, B., Tang, C., Brookes, P.C. and Xu, J., 2020. Long-term nutrient inputs shift soil microbial functional profiles of phosphorus cycling in diverse agroecosystems. The ISME journal, 14(3), pp.757-770.
'''Abstract'''
Microorganisms play an important role in soil phosphorus (P) cycling and regulation of P availability in agroecosystems. However, the responses of the functional and ecological traits of P-transformation microorganisms to long-term nutrient inputs are largely unknown. This study used metagenomics to investigate changes in the relative abundance of microbial P-transformation genes at four long-term experimental sites that received various inputs of N and P nutrients (up to 39 years). Long-term P input increased microbial P immobilization by decreasing the relative abundance of the P-starvation response gene (phoR) and increasing that of the low-affinity inorganic phosphate transporter gene (pit). This contrasts with previous findings that low-P conditions facilitate P immobilization in culturable microorganisms in short-term studies. In comparison, long-term nitrogen (N) input significantly decreased soil pH, and consequently decreased the relative abundances of total microbial P-solubilizing genes and the abundances of Actinobacteria, Gammaproteobacteria, and Alphaproteobacteria containing genes coding for alkaline phosphatase, and weakened the connection of relevant key genes. This challenges the concept that microbial P-solubilization capacity is mainly regulated by N:P stoichiometry. It is concluded that long-term N inputs decreased microbial P-solubilizing and mineralizing capacity while P inputs favored microbial immobilization via altering the microbial functional profiles, providing a novel insight into the regulation of P cycling in sustainable agroecosystems from a microbial perspective.

==Diptera==
===Wing and leg-waving behavior in flies===
====Food detection====
*''Rhagio lineola'' and ''R. tringarius'' feed on pollen and/or honeydew, which they locate by sweeping their front legs across the surface of leaves. They have a few fine hairs on their front legs, probably for this purpose. Other Rhagionidae do not have these hairs. 
**https://www.researchgate.net/publication/359760392
*It is also possible that some flies sample the air with the chemical sensors on their legs or feet.
**https://bugguide.net/node/view/217136/bgpage
====Courtship====
*Some Taeniapterinae are thought to wave their white-tipped front legs attract females.
**https://bugguide.net/node/view/217136/bgpage
*''Physiphora clausa'' appear to use leg-waving in courtship displays.
**https://www.flickr.com/photos/jean_hort/4663220062
*Waving of forelegs is included in the complex courtship behavior of ''Physiphora demandata''
**https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1439-0310.1979.tb00298.x
====Mimics for defense====
*Stilt-legged flies ''Rainieria antennaepes'' mimic ichneumonid wasps. They extend their fore-legs in front of their head, so they look like wasp antennae.
**https://thingsbiological.wordpress.com/2012/05/21/stilt-legged-flies-rainieria-antennaepes/ 
*Some hover-fly species mimic wasps by mock stinging, leg waving, or wing wagging.
**https://www.jstor.org/stable/10.1086/674612
*Wing-waving to mimic salticid spiders.
**https://www.researchgate.net/publication/27373081 https://www.researchgate.net/publication/6083895&lt;br&gt;
&lt;br&gt;

===Number of iNat records in Acalyptrate fly families===
The [[w:acalyptratae|acalyptrate fly clade]] includes the following superfamilies and families:&lt;br&gt;

* '''Carnoidea'''
** Acartophthalmidae         0
** Australimyzidae           0
** Braulidae (bee lice)         1
** Canacidae (beach flies)         3
** Carnidae (bird flies)         0
** Chloropidae (frit flies)         259
** Cryptochetidae              1
** Inbiomyiidae                0
** Milichiidae (freeloader flies) 158
&lt;br&gt;
* '''Diopsoidea'''
** Diopsidae (stalk-eyed flies)    545
** Gobryidae                   0
** Megamerinidae               0
** Nothybidae                   0
** Psilidae (rust flies)         29
** Somatiidae                   0
** Syringogastridae            0
&lt;br&gt;
* '''Ephydroidea'''
** Camillidae  0
** Campichoetidae   0
** Curtonotidae (quasimodo flies)   15
** Diastatidae 0
** Drosophilidae (vinegar and fruit flies) 312
** Ephydridae (shore flies) 117
&lt;br&gt;
* '''Lauxanioidea'''
** Celyphidae (beetle flies)  0
** Chamaemyiidae (aphid flies)  24
** Cremifaniidae  0
** Lauxaniidae (lauxaniid flies)  710
&lt;br&gt;
* '''Nerioidea'''
** Cypselosomatidae  0
** Fergusoninidae  0
** Micropezidae (stilt-legged flies)  245
** Neriidae  109
** Strongylophthalmyiidae  0
** Tanypezidae (stretched-foot flies)  0
&lt;br&gt;
* '''Opomyzoidea'''
** Agromyzidae (leaf-miner flies) 161
** Anthomyzidae  3
** Asteiidae  4
** Aulacigastridae  2
** Clusiidae (druid flies) 2
** Marginidae  0
** Neminidae 0 
** Neurochaetidae 0
** Odiniidae  0
** Opomyzidae  4
** Periscelididae  1
** Teratomyzidae  0
** Xenasteiidae  0
&lt;br&gt;
* '''Sciomyzoidea''' 
** Coelopidae (kelp flies)  51
** Conopidae (thick-headed flies)  192
** Dryomyzidae  1
** Helcomyzidae  0
** Helosciomyzidae  0
** Heterocheilidae  0
** Huttoninidae  0
** Natalimyzidae  0
** Phaeomyiidae  0
** Ropalomeridae  1
** Sciomyzidae (marsh flies)  67
** Sepsidae (black scavenger flies)  269
&lt;br&gt;
* '''Sphaeroceroidea'''
** Chyromyidae (golden flies)  19
** Heleomyzidae (heleomyzid flies)  151
** Nannodastiidae  0
** Sphaeroceridae (lesser dung flies)  48
&lt;br&gt;
* '''Tephritoidea'''
** Ctenostylidae  1
** Lonchaeidae (lance flies) 47
** Pallopteridae (flutter-wing flies)  5
** Piophilidae (cheese skipper flies) 1
** Platystomatidae (signal flies)  683
** Pyrgotidae (scarab-pursuing flies)  119
** Richardiidae  0
** Tachiniscidae  2
** Tephritidae (fruit flies)  1,759
** Ulidiidae (picture-winged flies) 165

== References ==</text>
      <sha1>m17hxtdkd2go1y0xqdfm258ybjwjw0u</sha1>
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        <id>1669821</id>
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      <comment>/* Genus Belarnoldus Antropov, 2007Antropov, A. V. (2007). On the taxonomy of South African digger wasps of the tribe Oxybelini (Hymenoptera, Crabronidae). Entomological Review, 87(4), 413-430. https://link.springer.com/article/10.1134/S0013873807040045 */</comment>
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= South African wasp species of Tribe Oxybelini ([[African Arthropods/Crabroninae|Crabronidae]])=
Bohart and Menke (1976)&lt;ref name BohartMenke1976&gt;Bohart, R.M. &amp; Menke, A. S. 1976. Sphecid Wasps of the World: a Generic Revision. University of California Press, Berkeley, California. pp. 359-370 https://archive.org/details/bub_gb_FExMjuRhjpIC/page/n359/mode/2up&lt;/ref&gt; reviewed the tribe, as did Antropov (1999-2007).
== Genus Belarnoldus Antropov, 2007&lt;ref name=Antropov2007&gt;Antropov, A. V. (2007). On the taxonomy of South African digger wasps of the tribe Oxybelini (Hymenoptera, Crabronidae). Entomological Review, 87(4), 413-430. https://link.springer.com/article/10.1134/S0013873807040045 [http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Antropov_2007b_Nototis_et_al_Eng.pdf PDF]&lt;/ref&gt;  ==

Belarnoldus crassus Arnold, 1936 (South Africa)

== Genus Belokohlus Antropov, 2007 ==

Belokohlus ferrieri (Kohl, 1924) (South Africa)

== Genus Belomicrinus Antropov, 2000 ==

Belomicrinus luteosquamatus Antropov, 2000 (Namibia)

Belomicrinus minutissimus (Arnold, 1936) (Namibia)

== Genus Belomicroides Kohl, 1899 ==

Belomicroides arenarius Arnold, 1960 (Zimbabwe)

Belomicroides clypeatus Antropov, 2002 (South Africa)

Belomicroides erythrogaster Antropov, 2002 (Namibia)

Belomicroides marleyi Arnold, 1927 (South Africa)

Belomicroides maximiliani Antropov, 2002 (Namibia)

Belomicroides pictus Arnold, 1927 (South Africa)

Belomicroides pictus chrysoptilus Antropov, 2002 (Namibia)

Belomicroides politus Antropov, 2002 (Namibia)

Belomicroides rift Antropov, 2002 (Kenya)

Belomicroides veronicae Antropov, 2002 (Ethiopia)

Belomicroides woji Antropov, 2002 (Namibia)

== Genus Belomicrus Costa, 1867 ==

Belomicrus mirificus Kohl, 1905 (Ethiopia)

== Genus Brimocelus Arnold, 1927 ==

Brimocelus radiatus (Arnold, 1927) (South Africa)

Brimocelus roosevelti Antropov, 2000 (South Africa)

Brimocelus schwarzi Antropov, 2000 (Namibia)

== Genus Gessus Antropov, 2001 ==

Gessus capensis Antropov, 2001 (South Africa)

== Genus Minimicroides Antropov, 2000 ==

Minimicroides perexiguus Antropov, 2000 (Namibia)

== Genus Nototis Arnold, 1927 ==

Nototis bicornutus Arnold, 1927 (South Africa)

Nototis falcidens Antropov, 2007 (Namibia)

== Genus Oxybelomorpha Brauns, 1897 ==

Oxybelomorpha braunsii (Kohl, 1923) (South Africa)

Oxybelomorpha funesta (Arnold, 1929) (South Africa)

Oxybelomorpha gessi Antropov, 2005 (South Africa)

Oxybelomorpha imitans Antropov, 2005 (South Africa)

Oxybelomorpha kohlii Brauns in Kohl, 1896 (South Africa)

Oxybelomorpha nitens Antropov, 2005 (South Africa)

Oxybelomorpha pseudosordida Antropov, 2005 (Namibia)

Oxybelomorpha pulawskii Antropov, 2005 (South Africa)

Oxybelomorpha rhodesiana (Arnold, 1927) (Zimbabwe)

Oxybelomorpha rubicunda Antropov, 2005 (Namibia)

Oxybelomorpha rufiventris (Arnold, 1936) (South Africa)

Oxybelomorpha separata Antropov, 2005 (South Africa)

Oxybelomorpha sgessae Antropov, 2005 (South Africa)

Oxybelomorpha sordida (Arnold, 1927) (South Africa)

Oxybelomorpha turneri (Arnold, 1927) (South Africa)

Oxybelomorpha wojciechi Antropov, 2005 (Namibia)

== Genus Oxybelus Latreille, 1796 ==

Oxybelus acutissimus Bischoff, 1912 (Democratic Republic of Congo)

Oxybelus acutissimus propinquus Arnold, 1927 (Zimbabwe)

Oxybelus aethiopicus Cameron, 1906 (South Africa)

Oxybelus angustus de Saussure, 1892 (South Africa)

Oxybelus arnoldi Benoit, 1951 (Democratic Republic of Congo)

Oxybelus bechuanae Arnold, 1936 (Botswana)

Oxybelus bicornutus Arnold, 1929 (Namibia, South Africa)

Oxybelus braunsi Arnold, 1927 (South Africa)

Oxybelus congophilus Benoit, 1951 (Democratic Republic of Congo)

Oxybelus coniferus Arnold, 1951 (Ethiopia)

Oxybelus cristatus de Saussure, 1892 (Madagascar)

Oxybelus curviscutis Arnold, 1927 (Zimbabwe)

Oxybelus dissimilis Arnold, 1934 (Zimbabwe)

Oxybelus eburneoguttatus Arnold, 1952 (Zimbabwe)

Oxybelus flavicornis Arnold, 1927 (Zimbabwe)

Oxybelus flavicornis nyassae Arnold, 1927 (Tanzania)

Oxybelus flaviventris Arnold, 1927 (Zimbabwe)

Oxybelus fraudulentus Arnold, 1929 (Namibia)

Oxybelus harraricus Arnold, 1927 (Ethiopia)

Oxybelus hessei Arnold, 1929 (Namibia)

Oxybelus imperialis Gerstaecker, 1867 (South Africa)

Oxybelus lepturus Arnold, 1927 (Zimbabwe)

Oxybelus limatus Arnold, 1927 (Zimbabwe)

Oxybelus lingula Gerstaecker, 1867 (South Africa)

Oxybelus matabele Arnold, 1927 (Zimbabwe)

Oxybelus metopias Kohl, 1894 (Mozambique)

Oxybelus nasutus Bischoff, 1913 (Namibia)

Oxybelus natalensis Arnold, 1927 (South Africa)

Oxybelus neuvillei Magretti, 1908 (Kenya)

Oxybelus pallidus Arnold, 1927 (Ethiopia, Tanzania)

Oxybelus paucipunctatus Arnold, 1927 (Zimbabwe)

Oxybelus peringueyi de Saussure, 1892 (South Africa)

Oxybelus perornatus Arnold, 1945 (Madagascar)

Oxybelus pictus Arnold, 1927 (Zimbabwe)

Oxybelus pilosus Arnold, 1927 (Ethiopia)

Oxybelus rubrocaudatus Arnold, 1927 (Zimbabwe)

Oxybelus ruficaudis Cameron, 1905 (South Africa)

Oxybelus ruficaudis melanarius Arnold, 1927 (South Africa)

Oxybelus solitarius Arnold, 1927 (Zimbabwe)

Oxybelus stevensoni Arnold, 1927 (Zimbabwe)

Oxybelus subcristatus de Saussure, 1892 (Madagascar)

Oxybelus taschenbergi Kohl, 1875 (South Africa)

Oxybelus willowmorensis Arnold, 1927 (South Africa)

Oxybelus woosnami Arnold, 1927 (Botswana, South Africa)

Oxybelus zavattarii Guiglia, 1943 (Ethiopia)

== Genus Wojus Antropov, 1999 ==

Wojus inopinatus Antropov, 1999 (South Africa)&lt;br&gt;
&lt;br&gt;

= South African wasp species of Subtribe Gastrosericina ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus ''Gastrosericus'' ==
There are 25 Afrotropical species; four in South Africa.

== Genus ''Kohliella'' Brauns, 1910 &lt;ref&gt;http://www.biodiversitylibrary.org/page/35572001&lt;/ref&gt;==

There are three species of ''Kohliella''; two are Afrotropical.&lt;ref&gt;https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm&lt;/ref&gt; 

''Kohliella alaris'' is found in South Africa and Zimbabwe; it hunts tree crickets.&lt;ref&gt;Gess, S.K. &amp; Gess, F.W. 2014. Wasps and bees in southern Africa. SANBI Biodiversity Series 24. South African National Biodiversity Institute, Pretoria. p. 71-72. https://archive.org/details/waspsbeesinsouth24gess/page/70/mode/2up&lt;/ref&gt;

== Genus ''Parapiagetia'' ==


== Genus ''Tachytes'' ==
There are 79 Afrotropical species; 15 in South Africa.

== Genus ''Tachysphex '' ==
There are 128 Afrotropical species; 41 in South Africa.

== Genus ''Larropsis '' ==

''Larropsis (Ancistromma) obliqua'' (F. Smith); description in Arnold, 1923b:218 as ''Tachytes obliquus''
== Genus ''Tachytella '' ==
== Genus ''Prosopigastra'' ==
== Genus ''Holotachysphex '' ==
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;


= Southern African wasp species of Tribe Trypoxylini ([[African Arthropods/Crabroninae|Crabronidae]]) =

== Genus ''Pison'' Jurine, 1808 ==

Arnold ([http://www.biodiversitylibrary.org/page/60327574 1924, 1-10]) has a key and descriptions.

*''Pison allonymum'' Schulz, 1906 (South Africa; probably most of southern Africa)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance 1.5 to 2.5 times the diameter of an ocellus;
**Fairly long, whitish or silvery pilosity on head and thorax, more dense on the temples than elsewhere.&lt;ref name=Arnold1924&gt;Arnold, G. (1924) The Sphegidae of South Africa. Part V. Annals of the Transvaal Museum 11:1-4 http://www.biodiversitylibrary.org/page/60327575&lt;/ref&gt;

*''Pison atrum'' (Spinola, 1808:253) described by Cameron as ''Pison montanum'' (Kenya, South Africa, Zambia)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance not greater than the diameter of an ocellus;
**Pronotal collar longer than in ''allonymum''.

*''Pison transvaalense'' Cameron, 1910 (South Africa; probably most of southern Africa to Tanzania and Uganda)
**Head and thorax dull; finely and closely punctured;
**Distance between the posterior ocelli and the eyes is equal to a third to a half of the diameter of the ocellus.


*''Pison auratum'' Shuckard, 1838 (an Australian species; see Pulawski, 2018:85 http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Pulawski_2018.pdf)

*''Pison denticeps'' Cameron, 1910 (South Africa; &quot;Transvaal&quot;. Two cubital cells; he only record seems to be the description)

*''Pison repentinum'' Arnold, 1940 (Zimbabwe)

*''Pison rufitarse'' Arnold, 1944 (Zimbabwe)

*''Pison scruposum'' Arnold, 1955 (Zimbabwe)

== Genus ''Trypoxylon'' Latreille, 1796 ==

*''Trypoxylon abditum'' Arnold, 1924 (South Africa)

*''Trypoxylon algoense'' Arnold, 1924 (South Africa)

*''Trypoxylon arnoldi'' Menke, 1976 (South Africa, Tanzania)

*''Trypoxylon braunsi'' Arnold, 1924 (South Africa)

*''Trypoxylon capense'' Cameron, 1905 (South Africa)

*''Trypoxylon cataractae'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon chirindense'' Arnold, 1936 (Burundi, Democratic Republic of Congo, Rwanda, Uganda, Zimbabwe)

*''Trypoxylon foveatum'' Cameron, 1904 (South Africa)

*''Trypoxylon inconstans'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon infimum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon kohli'' Arnold, 1924 (South Africa)

*''Trypoxylon letiferum'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon lissonotum'' Cameron, 1910 (South Africa)

*''Trypoxylon montivagum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon nodosum'' Arnold, 1944 (Zimbabwe)

*''Trypoxylon punctatissimum'' Arnold, 1924 (South Africa)

*''Trypoxylon stevensoni'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon stroudi'' Gribodo, 1884 (Ethiopia, South Africa, Democratic Republic of Congo)

*''Trypoxylon testaceipes'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon triste'' Arnold, 1924 (Zimbabwe)

= Pompilidae of South Africa =
== South African Pompilidae with fore-wings mainly orange to yellow with fuscous (darker or blackish) wing-tips ==
&lt;gallery mode=packed heights=200&gt;
Inaturalist 258649905 b.jpg
Hemipepsis hilaris - inaturalist 10850475.jpg
Cyphononyx decipiens inat 26259647 b.jpg
Tachypompilus ignitus inaturalist 311015843 02.jpg
Pompilidae 2021 12 12 inaturalist 313386858 04.jpg
Pompilidae 2020 04 13 inaturalist 43563902 06.jpg
&lt;/gallery&gt;
*The extent of the fuscous colour can be limited to the apex of the wing beyond the cells, or extend into the cells to a varying extent.
*
&lt;br&gt;

== South African Pompilidae with fore-wings fuscous (black or very dark) ==
*The wings often have green-blue-violet reflections.
&lt;gallery mode=packed heights=200&gt;
Pompilidae 2019 05 01 2835.jpg|Female ''Batozonellus fuliginosus''
Pompilidae inaturalist 124148802 01.jpg|Female ''Cyphononyx optimus''
Pompilidae 2021 12 18 iNat 316501919 a.jpg|Female ''Cyphononyx obscurus''
Pompilidae 2025 03 14 iNat 266538336 a.jpg|Male ''Hemipepsis vindex''
Pompilidae_2019_05_28_0256.jpg|
Spider-hunting Wasp (Hemipepsis) female (12640106905).jpg|''Hemipepsis'' sp.
&lt;/gallery&gt;

&lt;br&gt;
=== Species  with black antennae, legs, head, thorax and abdomen ===
Some parts may be brown.

*''Java atropos''
*''Cyphononyx obscurus''
*''Hemipepsis vindex''
*''Hemipepsis vespertilio''
*''Hemipepsis braunsi''
*''Batozonellus fuliginosus''
&lt;br&gt;
=== Species with black antennae, head, thorax and abdomen, but legs (or parts of some legs) yellow to red ===
*''Cyphononyx optimus''
*''Paracyphononyx zonatus''
&lt;br&gt;
&lt;br&gt;

== South African Pompilidae with fore-wings mainly hyaline to fuscous-hyaline ==
&lt;gallery mode=packed heights=200&gt;
Pompilidae inaturalist 123577538.jpg
Pompilidae inaturalist 46961473.jpg
Pompilidae iN 144781033 03.jpg

&lt;/gallery&gt;
*With fuscous (darker) wing apex
*One or two fuscous bands (faciated or bifaciated)
*Hyaline parts can be clouded (whiteish clouding) or coloured (yellow-tinted)


&lt;br&gt;
== South African Ceropalinae ==
Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region: [https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 Madl, 2020]
*''Ceropales africana'' Móczar, 1989. - {{font color||yellow|''helvetica'' group}} (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales cribrata cribrata'' A. Costa, 1881; key in Móczár 1986a: 321 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales {{font color||#0f0|(Priesnerius)}} gessi'' Móczar, 1988 (South Africa)
*''Ceropales {{font color||#0f0|(Priesnerius)}} grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales karooensis'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}} (Namibia, South Africa)
*''Ceropales kriechbaumeri'' Magretti, 1884 - {{font color||yellow|''helvetica'' group}} (Burkina Faso, Nigeria, South Africa?, Uganda, Zimbabwe?)
*''Ceropales {{font color||#0f0|(Priesnerius)}} kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Senegal, South Africa, Togo, Zimbabwe) 
*''Ceropales lawrencei'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales picta'' Shuckard, 1837; key in Móczár 1986b: 125 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus'' Cameron, 1904; key in Móczár 1986a: 320 (Lesotho, South Africa)
**''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
**''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
**= Hemiceropales scobinifera (Arnold, 1937): Móczár 1986a: 319
*''Ceropales (Bifidoceropales) sulciscutis'' Cameron, 1910; key in Móczár 1990: 61 (South Africa, Tanzania)
*''Ceropales waltoni'' Arnold, 1959 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989: 12 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
&lt;br&gt;

==Afrotropical Ceropalinae ==

Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region (Madl, 2020).&lt;ref name=Madl2020&gt;Madl, M. (2020). Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region. Zeitschrift der Arbeitsgemeinschaft Österreichischer Entomologen 72: 73-84.
[https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 PDF]&lt;/ref&gt;


Ceropalinae can be defined by:&lt;ref name=Brothers1993&gt;Brothers, D. J. &amp; Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. &amp; Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143&lt;/ref&gt;&lt;ref name=Waichert2015&gt; Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., &amp; Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287. {{doi|10.1111/zoj.12272}} [https://www.researchgate.net/publication/282015793 PDF]&lt;/ref&gt;

== Genera and species of Afrotropical Ceropalinae ==

This list is based on that of [https://www.waspweb.org/Pompiloidea/Pompilidae/Ceropalinae/index.htm '''waspweb'''] with changes following the Catalogue of Life (Kroupa &amp; Schmid-Egger, 2025)&lt;ref name=CoL2025&gt; Kroupa, A. S., &amp; Schmid-Egger, C. (2025). Hymenoptera Information System, Pompilidae of the World (version 2019-09). In O. Bánki, Y. Roskov, M. Döring, G. Ower, D. R. Hernández Robles, C. A. Plata Corredor, T. Stjernegaard Jeppesen, A. Örn, T. Pape, D. Hobern, S. Garnett, H. Little, R. E. DeWalt, J. Miller, T. Orrell, R. Aalbu, J. Abbott, C. Aedo, E. Aescht, et al., Catalogue of Life (Version 2025-07-10). Catalogue of Life Foundation, Amsterdam, Netherlands. https://doi.org/10.48580/dg9ld-4kv &lt;/ref&gt; and [[w:George_Arnold_(entomologist)|papers by Arnold (1932-1962)]].&lt;br&gt;

=== Genus ''Ceropales'' ===
*''Ceropales africana'' Móczar, 1989. (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales arnoldi'' Móczar, 1988 (Namibia)
*''Ceropales atra'' Móczar, 1991 (Botswana)
*''Ceropales cribrata cribrata'' A. Costa, 1881 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales cribrata maculipes'' Móczar, 1986 (Zambia)
*''Ceropales carinitifrons'' Wahis, 1986 (Madagascar)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales dayi'' Móczar, 1989 (Kenya)
*''Ceropales ferrugo'' Móczar, 1989 (Kenya)
*''Ceropales gambiae'' Móczar, 1989 (Burkina Faso, Cameroon, Democratic Republic of Congo, Gambia, Nigeria, Senegal, Sierra Leone)
*''Ceropales gessi'' Móczar, 1988 (South Africa)
*''Ceropales grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales juncoi'' Giner Mari, 1945 (Chad, Egypt, Israel, Pakistan, Somalia, Sudan, Western Sahara)
*''Ceropales karooensis'' Arnold, 1937 (Namibia, South Africa)
*''Ceropales kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Togo, Zimbabwe)
*''Ceropales kriechbaumeri'' Magretti, 1884 (Burkina Faso, Nigeria, South Africa, Uganda, Zimbabwe)
*''Ceropales latifasciatus'' Arnold, 1937 (Ethiopia)
*''Ceropales lawrencei'' Arnold, 1937 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales levipleuris'' Wahis, 1987 (Madagascar)
*''Ceropales maliensis'' Móczar, 1989 (Mali, Senegal)
*''Ceropales maroccana'' Beaumont, 1947 (Burkina Faso, Democratic Republic of Congo, Gambia, Ghana, Ivory Coast, Nigeria, Senegal, Zimbabwe. Also Palaearctic region)
*''Ceropales multipicta'' Arnold, 1937 (Botswana, Namibia)
*''Ceropales picta'' Shuckard, 1837 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus punctulatus'' Cameron, 1904 (Lesotho, South Africa)
*''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
*''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales ruficollis'' Cameron, 1910 (Kenya, Tanzania)
*''Ceropales saegeri'' Móczar, 1988 (Democratic Reublic of Congo)
*''Ceropales senegalensis'' Móczar, 1988 (Burkina Faso, Cameroon, Senegal)
**''Ceropales senegalensis mbouri'' Móczar, 1988 (Senegal)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
*''Ceropales seyrigi'' Wahis, 1987 (Madagascar)
*''Ceropales spinolai'' Móczar, 1988 (Guinea)
*''Ceropales subhelvetica'' Móczar, 1988 (Burkina Faso, Senegal. Also Palaearctic: Israel)
*''Ceropales sulciscutis'' Cameron, 1910 (South Africa, Tanzania)
**''Ceropales sulciscutis raymondi'' Móczar, 1990 (Democratic Republic of Congo)
*''Ceropales variolosus'' Arnold, 1937 (Democratic Republic of Congo, Ghana, Guinea, Mali, Nigeria, Senegal, Sudan, Togo, Uganda)
*''Ceropales waltoni'' Arnold, 1959 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
*''Ceropales yemeni'' Móczar, 1988 (Yemen. Also Palaearctic: Israel, Saudi Arabia)
&lt;br&gt;
=== Genus ''Irenangelus'' ===
*''Irenangelus madescassus'' Wahis, 1988 (Madagascar)
&lt;br&gt;

==Eumeninae==
Photos of ''Antodynerus'' on GBIF:&lt;br&gt;
''alboniger'': https://www.gbif.org/occurrence/1248689053 (CC BY-NC-SA 3.0)&lt;br&gt; 
''hova'': https://www.gbif.org/occurrence/1320165802 (CC0 1.0)&lt;br&gt;
''kelneri'': https://www.gbif.org/occurrence/3762658306 (CC BY-NC-SA 4.0)&lt;br&gt; 
''lugubris'': https://www.gbif.org/occurrence/1248689125 (CC BY-NC-SA 3.0)&lt;br&gt; 
''seyrigi'': https://www.gbif.org/occurrence/1322648015 (CC0 1.0)&lt;br&gt;
''sheffieldi'': https://www.gbif.org/occurrence/1318932924 (CC0 1.0)&lt;br&gt;
''silaos'': https://www.gbif.org/occurrence/1320574593 (CC0 1.0)&lt;br&gt;

==Ants==
'''Subfamilies of Formicidae (WaspWeb)'''

Number of iNaturalist records for subfamilies of Formicidae in Africa (2023-05-23)
Amblyoponinae              7
Dolichoderinae           630
Dorylinae                 1 167
Formicinae            10 396       Camponotus   6 090; Lepisiota 1 046
Myrmicinae              8 484       Crematogaster  1 786;   Pheidole  1 468;   Messor  1 156 
Ponerinae                1 623
Proceratiinae                  3
Pseudomyrmecinae   296


Aenictinae One Afrotropical genus ''Aenictus'' &lt;br&gt;

Aenictogitoninae One Afrotropical genus ''Aenictogiton'' &lt;br&gt;

Amblyoponinae Five Afrotropical genera &lt;br&gt;

Apomyrminae One Afrotropical genus ''Apomyrma'' &lt;br&gt; 

Cerapachyinae Five Afrotropical genera&lt;br&gt;

Dolichoderinae Eight Afrotropical genera&lt;br&gt;

Dorylinae One Afrotropical genus ''Dorylus'' &lt;br&gt;

Formicinae 20 Afrotropical genera&lt;br&gt;

Leptanillinae One Afrotropical genus ''Leptanilla'' &lt;br&gt;

Myrmicinae 37 Afrotropical genera &lt;br&gt;

Ponerinae 18 Afrotropical genera &lt;br&gt;

Proceratiinae Three Afrotropical genera  &lt;br&gt;

Pseudomyrmecinae One Afrotropical genus Tetraponera &lt;br&gt;


&lt;gallery mode=packed heights=200&gt;
Aenictogiton sp.jpg|''Aenictogiton'' sp., Aenictogitoninae 
Apomyrma stygia casent0101444 profile 1.jpg|''Apomyrma stygia'', Apomyrminae 
Cerapachys coxalis casent0173076 profile 1.jpg|''Cerapachys coxalis'', Cerapachyinae 
Cerapachys centurio castype12081-02 profile 1.jpg|''Cerapachys centurio'', Cerapachyinae
Tapinoma subtile casent0132840 dorsal 1.jpg|''Tapinoma subtile'', Dolichoderinae 
Dorylus helvolus, a, Seringveld.jpg|''Dorylus helvolus'', Dorylinae  
Polyrhachis schistacea00.jpg|''Polyrhachis schistacea'', Formicinae 
Anoplolepis custodiens, met prooi, a, Krugersdorp.jpg|''Anoplolepis custodiens'', Formicinae 
AFRICAN THIEF ANT SIX.jpg|''Carebara vidua'', Myrmicinae 
Millipede Hunter Ant (Plectroctena mandibularis) (11904420373).jpg|''Plectroctena mandibularis'', Ponerinae 
Discothyrea hewitti sam-hym-c000061a profile 1.jpg|''Discothyrea hewitti'', Proceratiinae 
Probolomyrmex filiformis casent0102141 profile 1.jpg|''Probolomyrmex filiformis'', Proceratiinae 
Slender Ant (Tetraponera natalensis) (30538051244).jpg|''Tetraponera natalensis'', Pseudomyrmecinae
&lt;/gallery&gt;

== N-P interactions ==
Dai, Z., Liu, G., Chen, H., Chen, C., Wang, J., Ai, S., Wei, D., Li, D., Ma, B., Tang, C., Brookes, P.C. and Xu, J., 2020. Long-term nutrient inputs shift soil microbial functional profiles of phosphorus cycling in diverse agroecosystems. The ISME journal, 14(3), pp.757-770.
'''Abstract'''
Microorganisms play an important role in soil phosphorus (P) cycling and regulation of P availability in agroecosystems. However, the responses of the functional and ecological traits of P-transformation microorganisms to long-term nutrient inputs are largely unknown. This study used metagenomics to investigate changes in the relative abundance of microbial P-transformation genes at four long-term experimental sites that received various inputs of N and P nutrients (up to 39 years). Long-term P input increased microbial P immobilization by decreasing the relative abundance of the P-starvation response gene (phoR) and increasing that of the low-affinity inorganic phosphate transporter gene (pit). This contrasts with previous findings that low-P conditions facilitate P immobilization in culturable microorganisms in short-term studies. In comparison, long-term nitrogen (N) input significantly decreased soil pH, and consequently decreased the relative abundances of total microbial P-solubilizing genes and the abundances of Actinobacteria, Gammaproteobacteria, and Alphaproteobacteria containing genes coding for alkaline phosphatase, and weakened the connection of relevant key genes. This challenges the concept that microbial P-solubilization capacity is mainly regulated by N:P stoichiometry. It is concluded that long-term N inputs decreased microbial P-solubilizing and mineralizing capacity while P inputs favored microbial immobilization via altering the microbial functional profiles, providing a novel insight into the regulation of P cycling in sustainable agroecosystems from a microbial perspective.

==Diptera==
===Wing and leg-waving behavior in flies===
====Food detection====
*''Rhagio lineola'' and ''R. tringarius'' feed on pollen and/or honeydew, which they locate by sweeping their front legs across the surface of leaves. They have a few fine hairs on their front legs, probably for this purpose. Other Rhagionidae do not have these hairs. 
**https://www.researchgate.net/publication/359760392
*It is also possible that some flies sample the air with the chemical sensors on their legs or feet.
**https://bugguide.net/node/view/217136/bgpage
====Courtship====
*Some Taeniapterinae are thought to wave their white-tipped front legs attract females.
**https://bugguide.net/node/view/217136/bgpage
*''Physiphora clausa'' appear to use leg-waving in courtship displays.
**https://www.flickr.com/photos/jean_hort/4663220062
*Waving of forelegs is included in the complex courtship behavior of ''Physiphora demandata''
**https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1439-0310.1979.tb00298.x
====Mimics for defense====
*Stilt-legged flies ''Rainieria antennaepes'' mimic ichneumonid wasps. They extend their fore-legs in front of their head, so they look like wasp antennae.
**https://thingsbiological.wordpress.com/2012/05/21/stilt-legged-flies-rainieria-antennaepes/ 
*Some hover-fly species mimic wasps by mock stinging, leg waving, or wing wagging.
**https://www.jstor.org/stable/10.1086/674612
*Wing-waving to mimic salticid spiders.
**https://www.researchgate.net/publication/27373081 https://www.researchgate.net/publication/6083895&lt;br&gt;
&lt;br&gt;

===Number of iNat records in Acalyptrate fly families===
The [[w:acalyptratae|acalyptrate fly clade]] includes the following superfamilies and families:&lt;br&gt;

* '''Carnoidea'''
** Acartophthalmidae         0
** Australimyzidae           0
** Braulidae (bee lice)         1
** Canacidae (beach flies)         3
** Carnidae (bird flies)         0
** Chloropidae (frit flies)         259
** Cryptochetidae              1
** Inbiomyiidae                0
** Milichiidae (freeloader flies) 158
&lt;br&gt;
* '''Diopsoidea'''
** Diopsidae (stalk-eyed flies)    545
** Gobryidae                   0
** Megamerinidae               0
** Nothybidae                   0
** Psilidae (rust flies)         29
** Somatiidae                   0
** Syringogastridae            0
&lt;br&gt;
* '''Ephydroidea'''
** Camillidae  0
** Campichoetidae   0
** Curtonotidae (quasimodo flies)   15
** Diastatidae 0
** Drosophilidae (vinegar and fruit flies) 312
** Ephydridae (shore flies) 117
&lt;br&gt;
* '''Lauxanioidea'''
** Celyphidae (beetle flies)  0
** Chamaemyiidae (aphid flies)  24
** Cremifaniidae  0
** Lauxaniidae (lauxaniid flies)  710
&lt;br&gt;
* '''Nerioidea'''
** Cypselosomatidae  0
** Fergusoninidae  0
** Micropezidae (stilt-legged flies)  245
** Neriidae  109
** Strongylophthalmyiidae  0
** Tanypezidae (stretched-foot flies)  0
&lt;br&gt;
* '''Opomyzoidea'''
** Agromyzidae (leaf-miner flies) 161
** Anthomyzidae  3
** Asteiidae  4
** Aulacigastridae  2
** Clusiidae (druid flies) 2
** Marginidae  0
** Neminidae 0 
** Neurochaetidae 0
** Odiniidae  0
** Opomyzidae  4
** Periscelididae  1
** Teratomyzidae  0
** Xenasteiidae  0
&lt;br&gt;
* '''Sciomyzoidea''' 
** Coelopidae (kelp flies)  51
** Conopidae (thick-headed flies)  192
** Dryomyzidae  1
** Helcomyzidae  0
** Helosciomyzidae  0
** Heterocheilidae  0
** Huttoninidae  0
** Natalimyzidae  0
** Phaeomyiidae  0
** Ropalomeridae  1
** Sciomyzidae (marsh flies)  67
** Sepsidae (black scavenger flies)  269
&lt;br&gt;
* '''Sphaeroceroidea'''
** Chyromyidae (golden flies)  19
** Heleomyzidae (heleomyzid flies)  151
** Nannodastiidae  0
** Sphaeroceridae (lesser dung flies)  48
&lt;br&gt;
* '''Tephritoidea'''
** Ctenostylidae  1
** Lonchaeidae (lance flies) 47
** Pallopteridae (flutter-wing flies)  5
** Piophilidae (cheese skipper flies) 1
** Platystomatidae (signal flies)  683
** Pyrgotidae (scarab-pursuing flies)  119
** Richardiidae  0
** Tachiniscidae  2
** Tephritidae (fruit flies)  1,759
** Ulidiidae (picture-winged flies) 165

== References ==</text>
      <sha1>l2jd4jwj6fi6pzoob7rzvr5k33c3vq9</sha1>
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        <id>1669821</id>
      </contributor>
      <comment>/* South African wasp species of Tribe Oxybelini (Crabronidae) */</comment>
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= South African wasp species of Tribe Oxybelini ([[African Arthropods/Crabroninae|Crabronidae]])=
Bohart and Menke (1976)&lt;ref name BohartMenke1976&gt;Bohart, R.M. &amp; Menke, A. S. 1976. Sphecid Wasps of the World: a Generic Revision. University of California Press, Berkeley, California. pp. 359-370 https://archive.org/details/bub_gb_FExMjuRhjpIC/page/n359/mode/2up&lt;/ref&gt; reviewed the tribe, as did Antropov (1999-2007).
== Genus ''Belarnoldus'' &lt;small&gt;Antropov, 2007&lt;ref name=Antropov2007&gt;Antropov, A. V. (2007). On the taxonomy of South African digger wasps of the tribe Oxybelini (Hymenoptera, Crabronidae). Entomological Review, 87(4), 413-430. https://link.springer.com/article/10.1134/S0013873807040045 [http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Antropov_2007b_Nototis_et_al_Eng.pdf PDF]&lt;/ref&gt;&lt;/small&gt;  ==

Belarnoldus crassus Arnold, 1936 (South Africa)

== Genus ''Belokohlus'' Antropov, 2007 ==

Belokohlus ferrieri (Kohl, 1924) (South Africa)

== Genus Belomicrinus Antropov, 2000 ==

Belomicrinus luteosquamatus Antropov, 2000 (Namibia)

Belomicrinus minutissimus (Arnold, 1936) (Namibia)

== Genus Belomicroides Kohl, 1899 ==

Belomicroides arenarius Arnold, 1960 (Zimbabwe)

Belomicroides clypeatus Antropov, 2002 (South Africa)

Belomicroides erythrogaster Antropov, 2002 (Namibia)

Belomicroides marleyi Arnold, 1927 (South Africa)

Belomicroides maximiliani Antropov, 2002 (Namibia)

Belomicroides pictus Arnold, 1927 (South Africa)

Belomicroides pictus chrysoptilus Antropov, 2002 (Namibia)

Belomicroides politus Antropov, 2002 (Namibia)

Belomicroides rift Antropov, 2002 (Kenya)

Belomicroides veronicae Antropov, 2002 (Ethiopia)

Belomicroides woji Antropov, 2002 (Namibia)

== Genus Belomicrus Costa, 1867 ==

Belomicrus mirificus Kohl, 1905 (Ethiopia)

== Genus Brimocelus Arnold, 1927 ==

Brimocelus radiatus (Arnold, 1927) (South Africa)

Brimocelus roosevelti Antropov, 2000 (South Africa)

Brimocelus schwarzi Antropov, 2000 (Namibia)

== Genus Gessus Antropov, 2001 ==

Gessus capensis Antropov, 2001 (South Africa)

== Genus Minimicroides Antropov, 2000 ==

Minimicroides perexiguus Antropov, 2000 (Namibia)

== Genus Nototis Arnold, 1927 ==

Nototis bicornutus Arnold, 1927 (South Africa)

Nototis falcidens Antropov, 2007 (Namibia)

== Genus Oxybelomorpha Brauns, 1897 ==

Oxybelomorpha braunsii (Kohl, 1923) (South Africa)

Oxybelomorpha funesta (Arnold, 1929) (South Africa)

Oxybelomorpha gessi Antropov, 2005 (South Africa)

Oxybelomorpha imitans Antropov, 2005 (South Africa)

Oxybelomorpha kohlii Brauns in Kohl, 1896 (South Africa)

Oxybelomorpha nitens Antropov, 2005 (South Africa)

Oxybelomorpha pseudosordida Antropov, 2005 (Namibia)

Oxybelomorpha pulawskii Antropov, 2005 (South Africa)

Oxybelomorpha rhodesiana (Arnold, 1927) (Zimbabwe)

Oxybelomorpha rubicunda Antropov, 2005 (Namibia)

Oxybelomorpha rufiventris (Arnold, 1936) (South Africa)

Oxybelomorpha separata Antropov, 2005 (South Africa)

Oxybelomorpha sgessae Antropov, 2005 (South Africa)

Oxybelomorpha sordida (Arnold, 1927) (South Africa)

Oxybelomorpha turneri (Arnold, 1927) (South Africa)

Oxybelomorpha wojciechi Antropov, 2005 (Namibia)

== Genus Oxybelus Latreille, 1796 ==

Oxybelus acutissimus Bischoff, 1912 (Democratic Republic of Congo)

Oxybelus acutissimus propinquus Arnold, 1927 (Zimbabwe)

Oxybelus aethiopicus Cameron, 1906 (South Africa)

Oxybelus angustus de Saussure, 1892 (South Africa)

Oxybelus arnoldi Benoit, 1951 (Democratic Republic of Congo)

Oxybelus bechuanae Arnold, 1936 (Botswana)

Oxybelus bicornutus Arnold, 1929 (Namibia, South Africa)

Oxybelus braunsi Arnold, 1927 (South Africa)

Oxybelus congophilus Benoit, 1951 (Democratic Republic of Congo)

Oxybelus coniferus Arnold, 1951 (Ethiopia)

Oxybelus cristatus de Saussure, 1892 (Madagascar)

Oxybelus curviscutis Arnold, 1927 (Zimbabwe)

Oxybelus dissimilis Arnold, 1934 (Zimbabwe)

Oxybelus eburneoguttatus Arnold, 1952 (Zimbabwe)

Oxybelus flavicornis Arnold, 1927 (Zimbabwe)

Oxybelus flavicornis nyassae Arnold, 1927 (Tanzania)

Oxybelus flaviventris Arnold, 1927 (Zimbabwe)

Oxybelus fraudulentus Arnold, 1929 (Namibia)

Oxybelus harraricus Arnold, 1927 (Ethiopia)

Oxybelus hessei Arnold, 1929 (Namibia)

Oxybelus imperialis Gerstaecker, 1867 (South Africa)

Oxybelus lepturus Arnold, 1927 (Zimbabwe)

Oxybelus limatus Arnold, 1927 (Zimbabwe)

Oxybelus lingula Gerstaecker, 1867 (South Africa)

Oxybelus matabele Arnold, 1927 (Zimbabwe)

Oxybelus metopias Kohl, 1894 (Mozambique)

Oxybelus nasutus Bischoff, 1913 (Namibia)

Oxybelus natalensis Arnold, 1927 (South Africa)

Oxybelus neuvillei Magretti, 1908 (Kenya)

Oxybelus pallidus Arnold, 1927 (Ethiopia, Tanzania)

Oxybelus paucipunctatus Arnold, 1927 (Zimbabwe)

Oxybelus peringueyi de Saussure, 1892 (South Africa)

Oxybelus perornatus Arnold, 1945 (Madagascar)

Oxybelus pictus Arnold, 1927 (Zimbabwe)

Oxybelus pilosus Arnold, 1927 (Ethiopia)

Oxybelus rubrocaudatus Arnold, 1927 (Zimbabwe)

Oxybelus ruficaudis Cameron, 1905 (South Africa)

Oxybelus ruficaudis melanarius Arnold, 1927 (South Africa)

Oxybelus solitarius Arnold, 1927 (Zimbabwe)

Oxybelus stevensoni Arnold, 1927 (Zimbabwe)

Oxybelus subcristatus de Saussure, 1892 (Madagascar)

Oxybelus taschenbergi Kohl, 1875 (South Africa)

Oxybelus willowmorensis Arnold, 1927 (South Africa)

Oxybelus woosnami Arnold, 1927 (Botswana, South Africa)

Oxybelus zavattarii Guiglia, 1943 (Ethiopia)

== Genus Wojus Antropov, 1999 ==

Wojus inopinatus Antropov, 1999 (South Africa)&lt;br&gt;
&lt;br&gt;

= South African wasp species of Subtribe Gastrosericina ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus ''Gastrosericus'' ==
There are 25 Afrotropical species; four in South Africa.

== Genus ''Kohliella'' Brauns, 1910 &lt;ref&gt;http://www.biodiversitylibrary.org/page/35572001&lt;/ref&gt;==

There are three species of ''Kohliella''; two are Afrotropical.&lt;ref&gt;https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm&lt;/ref&gt; 

''Kohliella alaris'' is found in South Africa and Zimbabwe; it hunts tree crickets.&lt;ref&gt;Gess, S.K. &amp; Gess, F.W. 2014. Wasps and bees in southern Africa. SANBI Biodiversity Series 24. South African National Biodiversity Institute, Pretoria. p. 71-72. https://archive.org/details/waspsbeesinsouth24gess/page/70/mode/2up&lt;/ref&gt;

== Genus ''Parapiagetia'' ==


== Genus ''Tachytes'' ==
There are 79 Afrotropical species; 15 in South Africa.

== Genus ''Tachysphex '' ==
There are 128 Afrotropical species; 41 in South Africa.

== Genus ''Larropsis '' ==

''Larropsis (Ancistromma) obliqua'' (F. Smith); description in Arnold, 1923b:218 as ''Tachytes obliquus''
== Genus ''Tachytella '' ==
== Genus ''Prosopigastra'' ==
== Genus ''Holotachysphex '' ==
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;


= Southern African wasp species of Tribe Trypoxylini ([[African Arthropods/Crabroninae|Crabronidae]]) =

== Genus ''Pison'' Jurine, 1808 ==

Arnold ([http://www.biodiversitylibrary.org/page/60327574 1924, 1-10]) has a key and descriptions.

*''Pison allonymum'' Schulz, 1906 (South Africa; probably most of southern Africa)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance 1.5 to 2.5 times the diameter of an ocellus;
**Fairly long, whitish or silvery pilosity on head and thorax, more dense on the temples than elsewhere.&lt;ref name=Arnold1924&gt;Arnold, G. (1924) The Sphegidae of South Africa. Part V. Annals of the Transvaal Museum 11:1-4 http://www.biodiversitylibrary.org/page/60327575&lt;/ref&gt;

*''Pison atrum'' (Spinola, 1808:253) described by Cameron as ''Pison montanum'' (Kenya, South Africa, Zambia)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance not greater than the diameter of an ocellus;
**Pronotal collar longer than in ''allonymum''.

*''Pison transvaalense'' Cameron, 1910 (South Africa; probably most of southern Africa to Tanzania and Uganda)
**Head and thorax dull; finely and closely punctured;
**Distance between the posterior ocelli and the eyes is equal to a third to a half of the diameter of the ocellus.


*''Pison auratum'' Shuckard, 1838 (an Australian species; see Pulawski, 2018:85 http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Pulawski_2018.pdf)

*''Pison denticeps'' Cameron, 1910 (South Africa; &quot;Transvaal&quot;. Two cubital cells; he only record seems to be the description)

*''Pison repentinum'' Arnold, 1940 (Zimbabwe)

*''Pison rufitarse'' Arnold, 1944 (Zimbabwe)

*''Pison scruposum'' Arnold, 1955 (Zimbabwe)

== Genus ''Trypoxylon'' Latreille, 1796 ==

*''Trypoxylon abditum'' Arnold, 1924 (South Africa)

*''Trypoxylon algoense'' Arnold, 1924 (South Africa)

*''Trypoxylon arnoldi'' Menke, 1976 (South Africa, Tanzania)

*''Trypoxylon braunsi'' Arnold, 1924 (South Africa)

*''Trypoxylon capense'' Cameron, 1905 (South Africa)

*''Trypoxylon cataractae'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon chirindense'' Arnold, 1936 (Burundi, Democratic Republic of Congo, Rwanda, Uganda, Zimbabwe)

*''Trypoxylon foveatum'' Cameron, 1904 (South Africa)

*''Trypoxylon inconstans'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon infimum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon kohli'' Arnold, 1924 (South Africa)

*''Trypoxylon letiferum'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon lissonotum'' Cameron, 1910 (South Africa)

*''Trypoxylon montivagum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon nodosum'' Arnold, 1944 (Zimbabwe)

*''Trypoxylon punctatissimum'' Arnold, 1924 (South Africa)

*''Trypoxylon stevensoni'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon stroudi'' Gribodo, 1884 (Ethiopia, South Africa, Democratic Republic of Congo)

*''Trypoxylon testaceipes'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon triste'' Arnold, 1924 (Zimbabwe)

= Pompilidae of South Africa =
== South African Pompilidae with fore-wings mainly orange to yellow with fuscous (darker or blackish) wing-tips ==
&lt;gallery mode=packed heights=200&gt;
Inaturalist 258649905 b.jpg
Hemipepsis hilaris - inaturalist 10850475.jpg
Cyphononyx decipiens inat 26259647 b.jpg
Tachypompilus ignitus inaturalist 311015843 02.jpg
Pompilidae 2021 12 12 inaturalist 313386858 04.jpg
Pompilidae 2020 04 13 inaturalist 43563902 06.jpg
&lt;/gallery&gt;
*The extent of the fuscous colour can be limited to the apex of the wing beyond the cells, or extend into the cells to a varying extent.
*
&lt;br&gt;

== South African Pompilidae with fore-wings fuscous (black or very dark) ==
*The wings often have green-blue-violet reflections.
&lt;gallery mode=packed heights=200&gt;
Pompilidae 2019 05 01 2835.jpg|Female ''Batozonellus fuliginosus''
Pompilidae inaturalist 124148802 01.jpg|Female ''Cyphononyx optimus''
Pompilidae 2021 12 18 iNat 316501919 a.jpg|Female ''Cyphononyx obscurus''
Pompilidae 2025 03 14 iNat 266538336 a.jpg|Male ''Hemipepsis vindex''
Pompilidae_2019_05_28_0256.jpg|
Spider-hunting Wasp (Hemipepsis) female (12640106905).jpg|''Hemipepsis'' sp.
&lt;/gallery&gt;

&lt;br&gt;
=== Species  with black antennae, legs, head, thorax and abdomen ===
Some parts may be brown.

*''Java atropos''
*''Cyphononyx obscurus''
*''Hemipepsis vindex''
*''Hemipepsis vespertilio''
*''Hemipepsis braunsi''
*''Batozonellus fuliginosus''
&lt;br&gt;
=== Species with black antennae, head, thorax and abdomen, but legs (or parts of some legs) yellow to red ===
*''Cyphononyx optimus''
*''Paracyphononyx zonatus''
&lt;br&gt;
&lt;br&gt;

== South African Pompilidae with fore-wings mainly hyaline to fuscous-hyaline ==
&lt;gallery mode=packed heights=200&gt;
Pompilidae inaturalist 123577538.jpg
Pompilidae inaturalist 46961473.jpg
Pompilidae iN 144781033 03.jpg

&lt;/gallery&gt;
*With fuscous (darker) wing apex
*One or two fuscous bands (faciated or bifaciated)
*Hyaline parts can be clouded (whiteish clouding) or coloured (yellow-tinted)


&lt;br&gt;
== South African Ceropalinae ==
Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region: [https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 Madl, 2020]
*''Ceropales africana'' Móczar, 1989. - {{font color||yellow|''helvetica'' group}} (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales cribrata cribrata'' A. Costa, 1881; key in Móczár 1986a: 321 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales {{font color||#0f0|(Priesnerius)}} gessi'' Móczar, 1988 (South Africa)
*''Ceropales {{font color||#0f0|(Priesnerius)}} grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales karooensis'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}} (Namibia, South Africa)
*''Ceropales kriechbaumeri'' Magretti, 1884 - {{font color||yellow|''helvetica'' group}} (Burkina Faso, Nigeria, South Africa?, Uganda, Zimbabwe?)
*''Ceropales {{font color||#0f0|(Priesnerius)}} kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Senegal, South Africa, Togo, Zimbabwe) 
*''Ceropales lawrencei'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales picta'' Shuckard, 1837; key in Móczár 1986b: 125 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus'' Cameron, 1904; key in Móczár 1986a: 320 (Lesotho, South Africa)
**''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
**''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
**= Hemiceropales scobinifera (Arnold, 1937): Móczár 1986a: 319
*''Ceropales (Bifidoceropales) sulciscutis'' Cameron, 1910; key in Móczár 1990: 61 (South Africa, Tanzania)
*''Ceropales waltoni'' Arnold, 1959 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989: 12 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
&lt;br&gt;

==Afrotropical Ceropalinae ==

Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region (Madl, 2020).&lt;ref name=Madl2020&gt;Madl, M. (2020). Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region. Zeitschrift der Arbeitsgemeinschaft Österreichischer Entomologen 72: 73-84.
[https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 PDF]&lt;/ref&gt;


Ceropalinae can be defined by:&lt;ref name=Brothers1993&gt;Brothers, D. J. &amp; Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. &amp; Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143&lt;/ref&gt;&lt;ref name=Waichert2015&gt; Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., &amp; Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287. {{doi|10.1111/zoj.12272}} [https://www.researchgate.net/publication/282015793 PDF]&lt;/ref&gt;

== Genera and species of Afrotropical Ceropalinae ==

This list is based on that of [https://www.waspweb.org/Pompiloidea/Pompilidae/Ceropalinae/index.htm '''waspweb'''] with changes following the Catalogue of Life (Kroupa &amp; Schmid-Egger, 2025)&lt;ref name=CoL2025&gt; Kroupa, A. S., &amp; Schmid-Egger, C. (2025). Hymenoptera Information System, Pompilidae of the World (version 2019-09). In O. Bánki, Y. Roskov, M. Döring, G. Ower, D. R. Hernández Robles, C. A. Plata Corredor, T. Stjernegaard Jeppesen, A. Örn, T. Pape, D. Hobern, S. Garnett, H. Little, R. E. DeWalt, J. Miller, T. Orrell, R. Aalbu, J. Abbott, C. Aedo, E. Aescht, et al., Catalogue of Life (Version 2025-07-10). Catalogue of Life Foundation, Amsterdam, Netherlands. https://doi.org/10.48580/dg9ld-4kv &lt;/ref&gt; and [[w:George_Arnold_(entomologist)|papers by Arnold (1932-1962)]].&lt;br&gt;

=== Genus ''Ceropales'' ===
*''Ceropales africana'' Móczar, 1989. (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales arnoldi'' Móczar, 1988 (Namibia)
*''Ceropales atra'' Móczar, 1991 (Botswana)
*''Ceropales cribrata cribrata'' A. Costa, 1881 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales cribrata maculipes'' Móczar, 1986 (Zambia)
*''Ceropales carinitifrons'' Wahis, 1986 (Madagascar)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales dayi'' Móczar, 1989 (Kenya)
*''Ceropales ferrugo'' Móczar, 1989 (Kenya)
*''Ceropales gambiae'' Móczar, 1989 (Burkina Faso, Cameroon, Democratic Republic of Congo, Gambia, Nigeria, Senegal, Sierra Leone)
*''Ceropales gessi'' Móczar, 1988 (South Africa)
*''Ceropales grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales juncoi'' Giner Mari, 1945 (Chad, Egypt, Israel, Pakistan, Somalia, Sudan, Western Sahara)
*''Ceropales karooensis'' Arnold, 1937 (Namibia, South Africa)
*''Ceropales kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Togo, Zimbabwe)
*''Ceropales kriechbaumeri'' Magretti, 1884 (Burkina Faso, Nigeria, South Africa, Uganda, Zimbabwe)
*''Ceropales latifasciatus'' Arnold, 1937 (Ethiopia)
*''Ceropales lawrencei'' Arnold, 1937 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales levipleuris'' Wahis, 1987 (Madagascar)
*''Ceropales maliensis'' Móczar, 1989 (Mali, Senegal)
*''Ceropales maroccana'' Beaumont, 1947 (Burkina Faso, Democratic Republic of Congo, Gambia, Ghana, Ivory Coast, Nigeria, Senegal, Zimbabwe. Also Palaearctic region)
*''Ceropales multipicta'' Arnold, 1937 (Botswana, Namibia)
*''Ceropales picta'' Shuckard, 1837 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus punctulatus'' Cameron, 1904 (Lesotho, South Africa)
*''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
*''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales ruficollis'' Cameron, 1910 (Kenya, Tanzania)
*''Ceropales saegeri'' Móczar, 1988 (Democratic Reublic of Congo)
*''Ceropales senegalensis'' Móczar, 1988 (Burkina Faso, Cameroon, Senegal)
**''Ceropales senegalensis mbouri'' Móczar, 1988 (Senegal)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
*''Ceropales seyrigi'' Wahis, 1987 (Madagascar)
*''Ceropales spinolai'' Móczar, 1988 (Guinea)
*''Ceropales subhelvetica'' Móczar, 1988 (Burkina Faso, Senegal. Also Palaearctic: Israel)
*''Ceropales sulciscutis'' Cameron, 1910 (South Africa, Tanzania)
**''Ceropales sulciscutis raymondi'' Móczar, 1990 (Democratic Republic of Congo)
*''Ceropales variolosus'' Arnold, 1937 (Democratic Republic of Congo, Ghana, Guinea, Mali, Nigeria, Senegal, Sudan, Togo, Uganda)
*''Ceropales waltoni'' Arnold, 1959 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
*''Ceropales yemeni'' Móczar, 1988 (Yemen. Also Palaearctic: Israel, Saudi Arabia)
&lt;br&gt;
=== Genus ''Irenangelus'' ===
*''Irenangelus madescassus'' Wahis, 1988 (Madagascar)
&lt;br&gt;

==Eumeninae==
Photos of ''Antodynerus'' on GBIF:&lt;br&gt;
''alboniger'': https://www.gbif.org/occurrence/1248689053 (CC BY-NC-SA 3.0)&lt;br&gt; 
''hova'': https://www.gbif.org/occurrence/1320165802 (CC0 1.0)&lt;br&gt;
''kelneri'': https://www.gbif.org/occurrence/3762658306 (CC BY-NC-SA 4.0)&lt;br&gt; 
''lugubris'': https://www.gbif.org/occurrence/1248689125 (CC BY-NC-SA 3.0)&lt;br&gt; 
''seyrigi'': https://www.gbif.org/occurrence/1322648015 (CC0 1.0)&lt;br&gt;
''sheffieldi'': https://www.gbif.org/occurrence/1318932924 (CC0 1.0)&lt;br&gt;
''silaos'': https://www.gbif.org/occurrence/1320574593 (CC0 1.0)&lt;br&gt;

==Ants==
'''Subfamilies of Formicidae (WaspWeb)'''

Number of iNaturalist records for subfamilies of Formicidae in Africa (2023-05-23)
Amblyoponinae              7
Dolichoderinae           630
Dorylinae                 1 167
Formicinae            10 396       Camponotus   6 090; Lepisiota 1 046
Myrmicinae              8 484       Crematogaster  1 786;   Pheidole  1 468;   Messor  1 156 
Ponerinae                1 623
Proceratiinae                  3
Pseudomyrmecinae   296


Aenictinae One Afrotropical genus ''Aenictus'' &lt;br&gt;

Aenictogitoninae One Afrotropical genus ''Aenictogiton'' &lt;br&gt;

Amblyoponinae Five Afrotropical genera &lt;br&gt;

Apomyrminae One Afrotropical genus ''Apomyrma'' &lt;br&gt; 

Cerapachyinae Five Afrotropical genera&lt;br&gt;

Dolichoderinae Eight Afrotropical genera&lt;br&gt;

Dorylinae One Afrotropical genus ''Dorylus'' &lt;br&gt;

Formicinae 20 Afrotropical genera&lt;br&gt;

Leptanillinae One Afrotropical genus ''Leptanilla'' &lt;br&gt;

Myrmicinae 37 Afrotropical genera &lt;br&gt;

Ponerinae 18 Afrotropical genera &lt;br&gt;

Proceratiinae Three Afrotropical genera  &lt;br&gt;

Pseudomyrmecinae One Afrotropical genus Tetraponera &lt;br&gt;


&lt;gallery mode=packed heights=200&gt;
Aenictogiton sp.jpg|''Aenictogiton'' sp., Aenictogitoninae 
Apomyrma stygia casent0101444 profile 1.jpg|''Apomyrma stygia'', Apomyrminae 
Cerapachys coxalis casent0173076 profile 1.jpg|''Cerapachys coxalis'', Cerapachyinae 
Cerapachys centurio castype12081-02 profile 1.jpg|''Cerapachys centurio'', Cerapachyinae
Tapinoma subtile casent0132840 dorsal 1.jpg|''Tapinoma subtile'', Dolichoderinae 
Dorylus helvolus, a, Seringveld.jpg|''Dorylus helvolus'', Dorylinae  
Polyrhachis schistacea00.jpg|''Polyrhachis schistacea'', Formicinae 
Anoplolepis custodiens, met prooi, a, Krugersdorp.jpg|''Anoplolepis custodiens'', Formicinae 
AFRICAN THIEF ANT SIX.jpg|''Carebara vidua'', Myrmicinae 
Millipede Hunter Ant (Plectroctena mandibularis) (11904420373).jpg|''Plectroctena mandibularis'', Ponerinae 
Discothyrea hewitti sam-hym-c000061a profile 1.jpg|''Discothyrea hewitti'', Proceratiinae 
Probolomyrmex filiformis casent0102141 profile 1.jpg|''Probolomyrmex filiformis'', Proceratiinae 
Slender Ant (Tetraponera natalensis) (30538051244).jpg|''Tetraponera natalensis'', Pseudomyrmecinae
&lt;/gallery&gt;

== N-P interactions ==
Dai, Z., Liu, G., Chen, H., Chen, C., Wang, J., Ai, S., Wei, D., Li, D., Ma, B., Tang, C., Brookes, P.C. and Xu, J., 2020. Long-term nutrient inputs shift soil microbial functional profiles of phosphorus cycling in diverse agroecosystems. The ISME journal, 14(3), pp.757-770.
'''Abstract'''
Microorganisms play an important role in soil phosphorus (P) cycling and regulation of P availability in agroecosystems. However, the responses of the functional and ecological traits of P-transformation microorganisms to long-term nutrient inputs are largely unknown. This study used metagenomics to investigate changes in the relative abundance of microbial P-transformation genes at four long-term experimental sites that received various inputs of N and P nutrients (up to 39 years). Long-term P input increased microbial P immobilization by decreasing the relative abundance of the P-starvation response gene (phoR) and increasing that of the low-affinity inorganic phosphate transporter gene (pit). This contrasts with previous findings that low-P conditions facilitate P immobilization in culturable microorganisms in short-term studies. In comparison, long-term nitrogen (N) input significantly decreased soil pH, and consequently decreased the relative abundances of total microbial P-solubilizing genes and the abundances of Actinobacteria, Gammaproteobacteria, and Alphaproteobacteria containing genes coding for alkaline phosphatase, and weakened the connection of relevant key genes. This challenges the concept that microbial P-solubilization capacity is mainly regulated by N:P stoichiometry. It is concluded that long-term N inputs decreased microbial P-solubilizing and mineralizing capacity while P inputs favored microbial immobilization via altering the microbial functional profiles, providing a novel insight into the regulation of P cycling in sustainable agroecosystems from a microbial perspective.

==Diptera==
===Wing and leg-waving behavior in flies===
====Food detection====
*''Rhagio lineola'' and ''R. tringarius'' feed on pollen and/or honeydew, which they locate by sweeping their front legs across the surface of leaves. They have a few fine hairs on their front legs, probably for this purpose. Other Rhagionidae do not have these hairs. 
**https://www.researchgate.net/publication/359760392
*It is also possible that some flies sample the air with the chemical sensors on their legs or feet.
**https://bugguide.net/node/view/217136/bgpage
====Courtship====
*Some Taeniapterinae are thought to wave their white-tipped front legs attract females.
**https://bugguide.net/node/view/217136/bgpage
*''Physiphora clausa'' appear to use leg-waving in courtship displays.
**https://www.flickr.com/photos/jean_hort/4663220062
*Waving of forelegs is included in the complex courtship behavior of ''Physiphora demandata''
**https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1439-0310.1979.tb00298.x
====Mimics for defense====
*Stilt-legged flies ''Rainieria antennaepes'' mimic ichneumonid wasps. They extend their fore-legs in front of their head, so they look like wasp antennae.
**https://thingsbiological.wordpress.com/2012/05/21/stilt-legged-flies-rainieria-antennaepes/ 
*Some hover-fly species mimic wasps by mock stinging, leg waving, or wing wagging.
**https://www.jstor.org/stable/10.1086/674612
*Wing-waving to mimic salticid spiders.
**https://www.researchgate.net/publication/27373081 https://www.researchgate.net/publication/6083895&lt;br&gt;
&lt;br&gt;

===Number of iNat records in Acalyptrate fly families===
The [[w:acalyptratae|acalyptrate fly clade]] includes the following superfamilies and families:&lt;br&gt;

* '''Carnoidea'''
** Acartophthalmidae         0
** Australimyzidae           0
** Braulidae (bee lice)         1
** Canacidae (beach flies)         3
** Carnidae (bird flies)         0
** Chloropidae (frit flies)         259
** Cryptochetidae              1
** Inbiomyiidae                0
** Milichiidae (freeloader flies) 158
&lt;br&gt;
* '''Diopsoidea'''
** Diopsidae (stalk-eyed flies)    545
** Gobryidae                   0
** Megamerinidae               0
** Nothybidae                   0
** Psilidae (rust flies)         29
** Somatiidae                   0
** Syringogastridae            0
&lt;br&gt;
* '''Ephydroidea'''
** Camillidae  0
** Campichoetidae   0
** Curtonotidae (quasimodo flies)   15
** Diastatidae 0
** Drosophilidae (vinegar and fruit flies) 312
** Ephydridae (shore flies) 117
&lt;br&gt;
* '''Lauxanioidea'''
** Celyphidae (beetle flies)  0
** Chamaemyiidae (aphid flies)  24
** Cremifaniidae  0
** Lauxaniidae (lauxaniid flies)  710
&lt;br&gt;
* '''Nerioidea'''
** Cypselosomatidae  0
** Fergusoninidae  0
** Micropezidae (stilt-legged flies)  245
** Neriidae  109
** Strongylophthalmyiidae  0
** Tanypezidae (stretched-foot flies)  0
&lt;br&gt;
* '''Opomyzoidea'''
** Agromyzidae (leaf-miner flies) 161
** Anthomyzidae  3
** Asteiidae  4
** Aulacigastridae  2
** Clusiidae (druid flies) 2
** Marginidae  0
** Neminidae 0 
** Neurochaetidae 0
** Odiniidae  0
** Opomyzidae  4
** Periscelididae  1
** Teratomyzidae  0
** Xenasteiidae  0
&lt;br&gt;
* '''Sciomyzoidea''' 
** Coelopidae (kelp flies)  51
** Conopidae (thick-headed flies)  192
** Dryomyzidae  1
** Helcomyzidae  0
** Helosciomyzidae  0
** Heterocheilidae  0
** Huttoninidae  0
** Natalimyzidae  0
** Phaeomyiidae  0
** Ropalomeridae  1
** Sciomyzidae (marsh flies)  67
** Sepsidae (black scavenger flies)  269
&lt;br&gt;
* '''Sphaeroceroidea'''
** Chyromyidae (golden flies)  19
** Heleomyzidae (heleomyzid flies)  151
** Nannodastiidae  0
** Sphaeroceridae (lesser dung flies)  48
&lt;br&gt;
* '''Tephritoidea'''
** Ctenostylidae  1
** Lonchaeidae (lance flies) 47
** Pallopteridae (flutter-wing flies)  5
** Piophilidae (cheese skipper flies) 1
** Platystomatidae (signal flies)  683
** Pyrgotidae (scarab-pursuing flies)  119
** Richardiidae  0
** Tachiniscidae  2
** Tephritidae (fruit flies)  1,759
** Ulidiidae (picture-winged flies) 165

== References ==</text>
      <sha1>s6cx5fav9yupcd3jf00dm6kto50y1c2</sha1>
    </revision>
    <revision>
      <id>2833758</id>
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      <contributor>
        <username>Alandmanson</username>
        <id>1669821</id>
      </contributor>
      <comment>/* South African wasp species of Tribe Oxybelini (Crabronidae) */</comment>
      <origin>2833758</origin>
      <model>wikitext</model>
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      <text bytes="29305" sha1="o76ij7gccndapc45ekonwoonu3u4m09" xml:space="preserve">&lt;!--Info--&gt;

= South African wasp species of Tribe Oxybelini ([[African Arthropods/Crabroninae|Crabronidae]])=
Bohart and Menke (1976)&lt;ref name BohartMenke1976&gt;Bohart, R.M. &amp; Menke, A. S. 1976. Sphecid Wasps of the World: a Generic Revision. University of California Press, Berkeley, California. pp. 359-370 https://archive.org/details/bub_gb_FExMjuRhjpIC/page/n359/mode/2up&lt;/ref&gt; reviewed the tribe, as did Antropov (1999-2007).
== Genus ''Belarnoldus'' &lt;small&gt;Antropov, 2007&lt;ref name=Antropov2007&gt;Antropov, A. V. (2007). On the taxonomy of South African digger wasps of the tribe Oxybelini (Hymenoptera, Crabronidae). Entomological Review, 87(4), 413-430. https://link.springer.com/article/10.1134/S0013873807040045 [http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Antropov_2007b_Nototis_et_al_Eng.pdf PDF]&lt;/ref&gt;&lt;/small&gt;  ==

''Belarnoldus crassus'' Arnold, 1936 (South Africa)

== Genus ''Belokohlus'' &lt;small&gt;Antropov, 2007&lt;ref name=Antropov2007&gt;Antropov, A. V. (2007). On the taxonomy of South African digger wasps of the tribe Oxybelini (Hymenoptera, Crabronidae). Entomological Review, 87(4), 413-430. https://link.springer.com/article/10.1134/S0013873807040045 [http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Antropov_2007b_Nototis_et_al_Eng.pdf PDF]&lt;/ref&gt;&lt;/small&gt; ==

''Belokohlus ferrieri'' (Kohl, 1924) (South Africa)

== Genus Belomicrinus Antropov, 2000 ==

Belomicrinus luteosquamatus Antropov, 2000 (Namibia)

Belomicrinus minutissimus (Arnold, 1936) (Namibia)

== Genus Belomicroides Kohl, 1899 ==

Belomicroides arenarius Arnold, 1960 (Zimbabwe)

Belomicroides clypeatus Antropov, 2002 (South Africa)

Belomicroides erythrogaster Antropov, 2002 (Namibia)

Belomicroides marleyi Arnold, 1927 (South Africa)

Belomicroides maximiliani Antropov, 2002 (Namibia)

Belomicroides pictus Arnold, 1927 (South Africa)

Belomicroides pictus chrysoptilus Antropov, 2002 (Namibia)

Belomicroides politus Antropov, 2002 (Namibia)

Belomicroides rift Antropov, 2002 (Kenya)

Belomicroides veronicae Antropov, 2002 (Ethiopia)

Belomicroides woji Antropov, 2002 (Namibia)

== Genus Belomicrus Costa, 1867 ==

Belomicrus mirificus Kohl, 1905 (Ethiopia)

== Genus Brimocelus Arnold, 1927 ==

Brimocelus radiatus (Arnold, 1927) (South Africa)

Brimocelus roosevelti Antropov, 2000 (South Africa)

Brimocelus schwarzi Antropov, 2000 (Namibia)

== Genus Gessus Antropov, 2001 ==

Gessus capensis Antropov, 2001 (South Africa)

== Genus Minimicroides Antropov, 2000 ==

Minimicroides perexiguus Antropov, 2000 (Namibia)

== Genus Nototis Arnold, 1927 ==

Nototis bicornutus Arnold, 1927 (South Africa)

Nototis falcidens Antropov, 2007 (Namibia)

== Genus Oxybelomorpha Brauns, 1897 ==

Oxybelomorpha braunsii (Kohl, 1923) (South Africa)

Oxybelomorpha funesta (Arnold, 1929) (South Africa)

Oxybelomorpha gessi Antropov, 2005 (South Africa)

Oxybelomorpha imitans Antropov, 2005 (South Africa)

Oxybelomorpha kohlii Brauns in Kohl, 1896 (South Africa)

Oxybelomorpha nitens Antropov, 2005 (South Africa)

Oxybelomorpha pseudosordida Antropov, 2005 (Namibia)

Oxybelomorpha pulawskii Antropov, 2005 (South Africa)

Oxybelomorpha rhodesiana (Arnold, 1927) (Zimbabwe)

Oxybelomorpha rubicunda Antropov, 2005 (Namibia)

Oxybelomorpha rufiventris (Arnold, 1936) (South Africa)

Oxybelomorpha separata Antropov, 2005 (South Africa)

Oxybelomorpha sgessae Antropov, 2005 (South Africa)

Oxybelomorpha sordida (Arnold, 1927) (South Africa)

Oxybelomorpha turneri (Arnold, 1927) (South Africa)

Oxybelomorpha wojciechi Antropov, 2005 (Namibia)

== Genus Oxybelus Latreille, 1796 ==

Oxybelus acutissimus Bischoff, 1912 (Democratic Republic of Congo)

Oxybelus acutissimus propinquus Arnold, 1927 (Zimbabwe)

Oxybelus aethiopicus Cameron, 1906 (South Africa)

Oxybelus angustus de Saussure, 1892 (South Africa)

Oxybelus arnoldi Benoit, 1951 (Democratic Republic of Congo)

Oxybelus bechuanae Arnold, 1936 (Botswana)

Oxybelus bicornutus Arnold, 1929 (Namibia, South Africa)

Oxybelus braunsi Arnold, 1927 (South Africa)

Oxybelus congophilus Benoit, 1951 (Democratic Republic of Congo)

Oxybelus coniferus Arnold, 1951 (Ethiopia)

Oxybelus cristatus de Saussure, 1892 (Madagascar)

Oxybelus curviscutis Arnold, 1927 (Zimbabwe)

Oxybelus dissimilis Arnold, 1934 (Zimbabwe)

Oxybelus eburneoguttatus Arnold, 1952 (Zimbabwe)

Oxybelus flavicornis Arnold, 1927 (Zimbabwe)

Oxybelus flavicornis nyassae Arnold, 1927 (Tanzania)

Oxybelus flaviventris Arnold, 1927 (Zimbabwe)

Oxybelus fraudulentus Arnold, 1929 (Namibia)

Oxybelus harraricus Arnold, 1927 (Ethiopia)

Oxybelus hessei Arnold, 1929 (Namibia)

Oxybelus imperialis Gerstaecker, 1867 (South Africa)

Oxybelus lepturus Arnold, 1927 (Zimbabwe)

Oxybelus limatus Arnold, 1927 (Zimbabwe)

Oxybelus lingula Gerstaecker, 1867 (South Africa)

Oxybelus matabele Arnold, 1927 (Zimbabwe)

Oxybelus metopias Kohl, 1894 (Mozambique)

Oxybelus nasutus Bischoff, 1913 (Namibia)

Oxybelus natalensis Arnold, 1927 (South Africa)

Oxybelus neuvillei Magretti, 1908 (Kenya)

Oxybelus pallidus Arnold, 1927 (Ethiopia, Tanzania)

Oxybelus paucipunctatus Arnold, 1927 (Zimbabwe)

Oxybelus peringueyi de Saussure, 1892 (South Africa)

Oxybelus perornatus Arnold, 1945 (Madagascar)

Oxybelus pictus Arnold, 1927 (Zimbabwe)

Oxybelus pilosus Arnold, 1927 (Ethiopia)

Oxybelus rubrocaudatus Arnold, 1927 (Zimbabwe)

Oxybelus ruficaudis Cameron, 1905 (South Africa)

Oxybelus ruficaudis melanarius Arnold, 1927 (South Africa)

Oxybelus solitarius Arnold, 1927 (Zimbabwe)

Oxybelus stevensoni Arnold, 1927 (Zimbabwe)

Oxybelus subcristatus de Saussure, 1892 (Madagascar)

Oxybelus taschenbergi Kohl, 1875 (South Africa)

Oxybelus willowmorensis Arnold, 1927 (South Africa)

Oxybelus woosnami Arnold, 1927 (Botswana, South Africa)

Oxybelus zavattarii Guiglia, 1943 (Ethiopia)

== Genus Wojus Antropov, 1999 ==

Wojus inopinatus Antropov, 1999 (South Africa)&lt;br&gt;
&lt;br&gt;

= South African wasp species of Subtribe Gastrosericina ([[African Arthropods/Crabroninae|Crabronidae]])=

== Genus ''Gastrosericus'' ==
There are 25 Afrotropical species; four in South Africa.

== Genus ''Kohliella'' Brauns, 1910 &lt;ref&gt;http://www.biodiversitylibrary.org/page/35572001&lt;/ref&gt;==

There are three species of ''Kohliella''; two are Afrotropical.&lt;ref&gt;https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm&lt;/ref&gt; 

''Kohliella alaris'' is found in South Africa and Zimbabwe; it hunts tree crickets.&lt;ref&gt;Gess, S.K. &amp; Gess, F.W. 2014. Wasps and bees in southern Africa. SANBI Biodiversity Series 24. South African National Biodiversity Institute, Pretoria. p. 71-72. https://archive.org/details/waspsbeesinsouth24gess/page/70/mode/2up&lt;/ref&gt;

== Genus ''Parapiagetia'' ==


== Genus ''Tachytes'' ==
There are 79 Afrotropical species; 15 in South Africa.

== Genus ''Tachysphex '' ==
There are 128 Afrotropical species; 41 in South Africa.

== Genus ''Larropsis '' ==

''Larropsis (Ancistromma) obliqua'' (F. Smith); description in Arnold, 1923b:218 as ''Tachytes obliquus''
== Genus ''Tachytella '' ==
== Genus ''Prosopigastra'' ==
== Genus ''Holotachysphex '' ==
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;
&lt;br&gt;


= Southern African wasp species of Tribe Trypoxylini ([[African Arthropods/Crabroninae|Crabronidae]]) =

== Genus ''Pison'' Jurine, 1808 ==

Arnold ([http://www.biodiversitylibrary.org/page/60327574 1924, 1-10]) has a key and descriptions.

*''Pison allonymum'' Schulz, 1906 (South Africa; probably most of southern Africa)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance 1.5 to 2.5 times the diameter of an ocellus;
**Fairly long, whitish or silvery pilosity on head and thorax, more dense on the temples than elsewhere.&lt;ref name=Arnold1924&gt;Arnold, G. (1924) The Sphegidae of South Africa. Part V. Annals of the Transvaal Museum 11:1-4 http://www.biodiversitylibrary.org/page/60327575&lt;/ref&gt;

*''Pison atrum'' (Spinola, 1808:253) described by Cameron as ''Pison montanum'' (Kenya, South Africa, Zambia)
**Head and thorax strongly punctured, the thorax more or less shining between the punctures; 
**Posterior ocelli separated from the eyes by a distance not greater than the diameter of an ocellus;
**Pronotal collar longer than in ''allonymum''.

*''Pison transvaalense'' Cameron, 1910 (South Africa; probably most of southern Africa to Tanzania and Uganda)
**Head and thorax dull; finely and closely punctured;
**Distance between the posterior ocelli and the eyes is equal to a third to a half of the diameter of the ocellus.


*''Pison auratum'' Shuckard, 1838 (an Australian species; see Pulawski, 2018:85 http://researcharchive.calacademy.org/research/entomology/Entomology_Resources/Hymenoptera/sphecidae/copies/Pulawski_2018.pdf)

*''Pison denticeps'' Cameron, 1910 (South Africa; &quot;Transvaal&quot;. Two cubital cells; he only record seems to be the description)

*''Pison repentinum'' Arnold, 1940 (Zimbabwe)

*''Pison rufitarse'' Arnold, 1944 (Zimbabwe)

*''Pison scruposum'' Arnold, 1955 (Zimbabwe)

== Genus ''Trypoxylon'' Latreille, 1796 ==

*''Trypoxylon abditum'' Arnold, 1924 (South Africa)

*''Trypoxylon algoense'' Arnold, 1924 (South Africa)

*''Trypoxylon arnoldi'' Menke, 1976 (South Africa, Tanzania)

*''Trypoxylon braunsi'' Arnold, 1924 (South Africa)

*''Trypoxylon capense'' Cameron, 1905 (South Africa)

*''Trypoxylon cataractae'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon chirindense'' Arnold, 1936 (Burundi, Democratic Republic of Congo, Rwanda, Uganda, Zimbabwe)

*''Trypoxylon foveatum'' Cameron, 1904 (South Africa)

*''Trypoxylon inconstans'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon infimum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon kohli'' Arnold, 1924 (South Africa)

*''Trypoxylon letiferum'' Arnold, 1946 (Zimbabwe)

*''Trypoxylon lissonotum'' Cameron, 1910 (South Africa)

*''Trypoxylon montivagum'' Arnold, 1940 (Zimbabwe)

*''Trypoxylon nodosum'' Arnold, 1944 (Zimbabwe)

*''Trypoxylon punctatissimum'' Arnold, 1924 (South Africa)

*''Trypoxylon stevensoni'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon stroudi'' Gribodo, 1884 (Ethiopia, South Africa, Democratic Republic of Congo)

*''Trypoxylon testaceipes'' Arnold, 1924 (Zimbabwe)

*''Trypoxylon triste'' Arnold, 1924 (Zimbabwe)

= Pompilidae of South Africa =
== South African Pompilidae with fore-wings mainly orange to yellow with fuscous (darker or blackish) wing-tips ==
&lt;gallery mode=packed heights=200&gt;
Inaturalist 258649905 b.jpg
Hemipepsis hilaris - inaturalist 10850475.jpg
Cyphononyx decipiens inat 26259647 b.jpg
Tachypompilus ignitus inaturalist 311015843 02.jpg
Pompilidae 2021 12 12 inaturalist 313386858 04.jpg
Pompilidae 2020 04 13 inaturalist 43563902 06.jpg
&lt;/gallery&gt;
*The extent of the fuscous colour can be limited to the apex of the wing beyond the cells, or extend into the cells to a varying extent.
*
&lt;br&gt;

== South African Pompilidae with fore-wings fuscous (black or very dark) ==
*The wings often have green-blue-violet reflections.
&lt;gallery mode=packed heights=200&gt;
Pompilidae 2019 05 01 2835.jpg|Female ''Batozonellus fuliginosus''
Pompilidae inaturalist 124148802 01.jpg|Female ''Cyphononyx optimus''
Pompilidae 2021 12 18 iNat 316501919 a.jpg|Female ''Cyphononyx obscurus''
Pompilidae 2025 03 14 iNat 266538336 a.jpg|Male ''Hemipepsis vindex''
Pompilidae_2019_05_28_0256.jpg|
Spider-hunting Wasp (Hemipepsis) female (12640106905).jpg|''Hemipepsis'' sp.
&lt;/gallery&gt;

&lt;br&gt;
=== Species  with black antennae, legs, head, thorax and abdomen ===
Some parts may be brown.

*''Java atropos''
*''Cyphononyx obscurus''
*''Hemipepsis vindex''
*''Hemipepsis vespertilio''
*''Hemipepsis braunsi''
*''Batozonellus fuliginosus''
&lt;br&gt;
=== Species with black antennae, head, thorax and abdomen, but legs (or parts of some legs) yellow to red ===
*''Cyphononyx optimus''
*''Paracyphononyx zonatus''
&lt;br&gt;
&lt;br&gt;

== South African Pompilidae with fore-wings mainly hyaline to fuscous-hyaline ==
&lt;gallery mode=packed heights=200&gt;
Pompilidae inaturalist 123577538.jpg
Pompilidae inaturalist 46961473.jpg
Pompilidae iN 144781033 03.jpg

&lt;/gallery&gt;
*With fuscous (darker) wing apex
*One or two fuscous bands (faciated or bifaciated)
*Hyaline parts can be clouded (whiteish clouding) or coloured (yellow-tinted)


&lt;br&gt;
== South African Ceropalinae ==
Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region: [https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 Madl, 2020]
*''Ceropales africana'' Móczar, 1989. - {{font color||yellow|''helvetica'' group}} (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales cribrata cribrata'' A. Costa, 1881; key in Móczár 1986a: 321 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales {{font color||#0f0|(Priesnerius)}} gessi'' Móczar, 1988 (South Africa)
*''Ceropales {{font color||#0f0|(Priesnerius)}} grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales karooensis'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}} (Namibia, South Africa)
*''Ceropales kriechbaumeri'' Magretti, 1884 - {{font color||yellow|''helvetica'' group}} (Burkina Faso, Nigeria, South Africa?, Uganda, Zimbabwe?)
*''Ceropales {{font color||#0f0|(Priesnerius)}} kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Senegal, South Africa, Togo, Zimbabwe) 
*''Ceropales lawrencei'' Arnold, 1937 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales picta'' Shuckard, 1837; key in Móczár 1986b: 125 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus'' Cameron, 1904; key in Móczár 1986a: 320 (Lesotho, South Africa)
**''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
**''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
**= Hemiceropales scobinifera (Arnold, 1937): Móczár 1986a: 319
*''Ceropales (Bifidoceropales) sulciscutis'' Cameron, 1910; key in Móczár 1990: 61 (South Africa, Tanzania)
*''Ceropales waltoni'' Arnold, 1959 - {{font color||yellow|''helvetica'' group}}; key in Móczár 1989: 12 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
&lt;br&gt;

==Afrotropical Ceropalinae ==

Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region (Madl, 2020).&lt;ref name=Madl2020&gt;Madl, M. (2020). Annotated catalogue of the subfamily Ceropalinae (Hymenoptera: Pompilidae) of the Afrotropical region. Zeitschrift der Arbeitsgemeinschaft Österreichischer Entomologen 72: 73-84.
[https://www.entomologie.at/permalink/articles/87-zeitschrift-der-arbeitsgemeinschaft-oesterreichischer-entomologen-72-2020-0073-0084 PDF]&lt;/ref&gt;


Ceropalinae can be defined by:&lt;ref name=Brothers1993&gt;Brothers, D. J. &amp; Finnamore. (1993). Superfamily Vespoidea. In Goulet, H. &amp; Huber, J. T. (Eds.). (1993). Hymenoptera of the world: an identification guide to families. 161-278. https://www.researchgate.net/publication/259227143&lt;/ref&gt;&lt;ref name=Waichert2015&gt; Waichert, C., Rodriguez, J., Wasbauer, M. S., Von Dohlen, C. D., &amp; Pitts, J. P. (2015). Molecular phylogeny and systematics of spider wasps (Hymenoptera: Pompilidae): redefining subfamily boundaries and the origin of the family. Zoological Journal of the Linnean Society, 175(2), 271-287. {{doi|10.1111/zoj.12272}} [https://www.researchgate.net/publication/282015793 PDF]&lt;/ref&gt;

== Genera and species of Afrotropical Ceropalinae ==

This list is based on that of [https://www.waspweb.org/Pompiloidea/Pompilidae/Ceropalinae/index.htm '''waspweb'''] with changes following the Catalogue of Life (Kroupa &amp; Schmid-Egger, 2025)&lt;ref name=CoL2025&gt; Kroupa, A. S., &amp; Schmid-Egger, C. (2025). Hymenoptera Information System, Pompilidae of the World (version 2019-09). In O. Bánki, Y. Roskov, M. Döring, G. Ower, D. R. Hernández Robles, C. A. Plata Corredor, T. Stjernegaard Jeppesen, A. Örn, T. Pape, D. Hobern, S. Garnett, H. Little, R. E. DeWalt, J. Miller, T. Orrell, R. Aalbu, J. Abbott, C. Aedo, E. Aescht, et al., Catalogue of Life (Version 2025-07-10). Catalogue of Life Foundation, Amsterdam, Netherlands. https://doi.org/10.48580/dg9ld-4kv &lt;/ref&gt; and [[w:George_Arnold_(entomologist)|papers by Arnold (1932-1962)]].&lt;br&gt;

=== Genus ''Ceropales'' ===
*''Ceropales africana'' Móczar, 1989. (Angola, Botswana, Burkina Faso, Central African Republic, Democratic Republic of Congo, Gabon, Gambia, Ghana, Ivory Coast, Kenya, Malawi, Namibia, Nigeria, Senegal, South Africa, Togo, Yemen, Zambia)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales arnoldi'' Móczar, 1988 (Namibia)
*''Ceropales atra'' Móczar, 1991 (Botswana)
*''Ceropales cribrata cribrata'' A. Costa, 1881 (Angola, Burkina Faso, Democratic Republic of Congo, Ivory Coast, Lesotho, Namibia, Nigeria, Russia, South Africa, Senegal, Tanzania, Togo, Zambia, Zimbabwe. Also Palaearctic region)
*''Ceropales cribrata maculipes'' Móczar, 1986 (Zambia)
*''Ceropales carinitifrons'' Wahis, 1986 (Madagascar)
*''Ceropales angolaensis'' Móczar, 1989 (Angola)
*''Ceropales dayi'' Móczar, 1989 (Kenya)
*''Ceropales ferrugo'' Móczar, 1989 (Kenya)
*''Ceropales gambiae'' Móczar, 1989 (Burkina Faso, Cameroon, Democratic Republic of Congo, Gambia, Nigeria, Senegal, Sierra Leone)
*''Ceropales gessi'' Móczar, 1988 (South Africa)
*''Ceropales grahamstowni'' Móczar, 1988 (South Africa, Zimbabwe)
*''Ceropales juncoi'' Giner Mari, 1945 (Chad, Egypt, Israel, Pakistan, Somalia, Sudan, Western Sahara)
*''Ceropales karooensis'' Arnold, 1937 (Namibia, South Africa)
*''Ceropales kongoensis'' Móczar, 1988 (Burkina Faso, Democratic Republic of Congo, Ghana, Togo, Zimbabwe)
*''Ceropales kriechbaumeri'' Magretti, 1884 (Burkina Faso, Nigeria, South Africa, Uganda, Zimbabwe)
*''Ceropales latifasciatus'' Arnold, 1937 (Ethiopia)
*''Ceropales lawrencei'' Arnold, 1937 (Botswana, Mozambique, South Africa, Zimbabwe)
*''Ceropales levipleuris'' Wahis, 1987 (Madagascar)
*''Ceropales maliensis'' Móczar, 1989 (Mali, Senegal)
*''Ceropales maroccana'' Beaumont, 1947 (Burkina Faso, Democratic Republic of Congo, Gambia, Ghana, Ivory Coast, Nigeria, Senegal, Zimbabwe. Also Palaearctic region)
*''Ceropales multipicta'' Arnold, 1937 (Botswana, Namibia)
*''Ceropales picta'' Shuckard, 1837 (Democratic Republic of Congo, Ethiopia, South Africa, Uganda)
*''Ceropales punctulatus punctulatus'' Cameron, 1904 (Lesotho, South Africa)
*''Ceropales punctulatus bulawayoensis'' Bischoff, 1913 (Angola, Burkina Faso, Congo, Democratic Republic of Congo, Gambia, Ghana, Lesotho, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda, Zimbabwe)
*''Ceropales punctulatus cereris'' Arnold, 1937 (Lesotho, South Africa)
*''Ceropales ruficollis'' Cameron, 1910 (Kenya, Tanzania)
*''Ceropales saegeri'' Móczar, 1988 (Democratic Reublic of Congo)
*''Ceropales senegalensis'' Móczar, 1988 (Burkina Faso, Cameroon, Senegal)
**''Ceropales senegalensis mbouri'' Móczar, 1988 (Senegal)
*''Ceropales scobiniferus'' Arnold, 1937 (Democratic Republic of Congo, Mozambique, Nigeria, South Africa)
*''Ceropales seyrigi'' Wahis, 1987 (Madagascar)
*''Ceropales spinolai'' Móczar, 1988 (Guinea)
*''Ceropales subhelvetica'' Móczar, 1988 (Burkina Faso, Senegal. Also Palaearctic: Israel)
*''Ceropales sulciscutis'' Cameron, 1910 (South Africa, Tanzania)
**''Ceropales sulciscutis raymondi'' Móczar, 1990 (Democratic Republic of Congo)
*''Ceropales variolosus'' Arnold, 1937 (Democratic Republic of Congo, Ghana, Guinea, Mali, Nigeria, Senegal, Sudan, Togo, Uganda)
*''Ceropales waltoni'' Arnold, 1959 (Botswana, Congo, Democratic Republic of Congo, Lesotho, South Africa, Zimbabwe)
*''Ceropales yemeni'' Móczar, 1988 (Yemen. Also Palaearctic: Israel, Saudi Arabia)
&lt;br&gt;
=== Genus ''Irenangelus'' ===
*''Irenangelus madescassus'' Wahis, 1988 (Madagascar)
&lt;br&gt;

==Eumeninae==
Photos of ''Antodynerus'' on GBIF:&lt;br&gt;
''alboniger'': https://www.gbif.org/occurrence/1248689053 (CC BY-NC-SA 3.0)&lt;br&gt; 
''hova'': https://www.gbif.org/occurrence/1320165802 (CC0 1.0)&lt;br&gt;
''kelneri'': https://www.gbif.org/occurrence/3762658306 (CC BY-NC-SA 4.0)&lt;br&gt; 
''lugubris'': https://www.gbif.org/occurrence/1248689125 (CC BY-NC-SA 3.0)&lt;br&gt; 
''seyrigi'': https://www.gbif.org/occurrence/1322648015 (CC0 1.0)&lt;br&gt;
''sheffieldi'': https://www.gbif.org/occurrence/1318932924 (CC0 1.0)&lt;br&gt;
''silaos'': https://www.gbif.org/occurrence/1320574593 (CC0 1.0)&lt;br&gt;

==Ants==
'''Subfamilies of Formicidae (WaspWeb)'''

Number of iNaturalist records for subfamilies of Formicidae in Africa (2023-05-23)
Amblyoponinae              7
Dolichoderinae           630
Dorylinae                 1 167
Formicinae            10 396       Camponotus   6 090; Lepisiota 1 046
Myrmicinae              8 484       Crematogaster  1 786;   Pheidole  1 468;   Messor  1 156 
Ponerinae                1 623
Proceratiinae                  3
Pseudomyrmecinae   296


Aenictinae One Afrotropical genus ''Aenictus'' &lt;br&gt;

Aenictogitoninae One Afrotropical genus ''Aenictogiton'' &lt;br&gt;

Amblyoponinae Five Afrotropical genera &lt;br&gt;

Apomyrminae One Afrotropical genus ''Apomyrma'' &lt;br&gt; 

Cerapachyinae Five Afrotropical genera&lt;br&gt;

Dolichoderinae Eight Afrotropical genera&lt;br&gt;

Dorylinae One Afrotropical genus ''Dorylus'' &lt;br&gt;

Formicinae 20 Afrotropical genera&lt;br&gt;

Leptanillinae One Afrotropical genus ''Leptanilla'' &lt;br&gt;

Myrmicinae 37 Afrotropical genera &lt;br&gt;

Ponerinae 18 Afrotropical genera &lt;br&gt;

Proceratiinae Three Afrotropical genera  &lt;br&gt;

Pseudomyrmecinae One Afrotropical genus Tetraponera &lt;br&gt;


&lt;gallery mode=packed heights=200&gt;
Aenictogiton sp.jpg|''Aenictogiton'' sp., Aenictogitoninae 
Apomyrma stygia casent0101444 profile 1.jpg|''Apomyrma stygia'', Apomyrminae 
Cerapachys coxalis casent0173076 profile 1.jpg|''Cerapachys coxalis'', Cerapachyinae 
Cerapachys centurio castype12081-02 profile 1.jpg|''Cerapachys centurio'', Cerapachyinae
Tapinoma subtile casent0132840 dorsal 1.jpg|''Tapinoma subtile'', Dolichoderinae 
Dorylus helvolus, a, Seringveld.jpg|''Dorylus helvolus'', Dorylinae  
Polyrhachis schistacea00.jpg|''Polyrhachis schistacea'', Formicinae 
Anoplolepis custodiens, met prooi, a, Krugersdorp.jpg|''Anoplolepis custodiens'', Formicinae 
AFRICAN THIEF ANT SIX.jpg|''Carebara vidua'', Myrmicinae 
Millipede Hunter Ant (Plectroctena mandibularis) (11904420373).jpg|''Plectroctena mandibularis'', Ponerinae 
Discothyrea hewitti sam-hym-c000061a profile 1.jpg|''Discothyrea hewitti'', Proceratiinae 
Probolomyrmex filiformis casent0102141 profile 1.jpg|''Probolomyrmex filiformis'', Proceratiinae 
Slender Ant (Tetraponera natalensis) (30538051244).jpg|''Tetraponera natalensis'', Pseudomyrmecinae
&lt;/gallery&gt;

== N-P interactions ==
Dai, Z., Liu, G., Chen, H., Chen, C., Wang, J., Ai, S., Wei, D., Li, D., Ma, B., Tang, C., Brookes, P.C. and Xu, J., 2020. Long-term nutrient inputs shift soil microbial functional profiles of phosphorus cycling in diverse agroecosystems. The ISME journal, 14(3), pp.757-770.
'''Abstract'''
Microorganisms play an important role in soil phosphorus (P) cycling and regulation of P availability in agroecosystems. However, the responses of the functional and ecological traits of P-transformation microorganisms to long-term nutrient inputs are largely unknown. This study used metagenomics to investigate changes in the relative abundance of microbial P-transformation genes at four long-term experimental sites that received various inputs of N and P nutrients (up to 39 years). Long-term P input increased microbial P immobilization by decreasing the relative abundance of the P-starvation response gene (phoR) and increasing that of the low-affinity inorganic phosphate transporter gene (pit). This contrasts with previous findings that low-P conditions facilitate P immobilization in culturable microorganisms in short-term studies. In comparison, long-term nitrogen (N) input significantly decreased soil pH, and consequently decreased the relative abundances of total microbial P-solubilizing genes and the abundances of Actinobacteria, Gammaproteobacteria, and Alphaproteobacteria containing genes coding for alkaline phosphatase, and weakened the connection of relevant key genes. This challenges the concept that microbial P-solubilization capacity is mainly regulated by N:P stoichiometry. It is concluded that long-term N inputs decreased microbial P-solubilizing and mineralizing capacity while P inputs favored microbial immobilization via altering the microbial functional profiles, providing a novel insight into the regulation of P cycling in sustainable agroecosystems from a microbial perspective.

==Diptera==
===Wing and leg-waving behavior in flies===
====Food detection====
*''Rhagio lineola'' and ''R. tringarius'' feed on pollen and/or honeydew, which they locate by sweeping their front legs across the surface of leaves. They have a few fine hairs on their front legs, probably for this purpose. Other Rhagionidae do not have these hairs. 
**https://www.researchgate.net/publication/359760392
*It is also possible that some flies sample the air with the chemical sensors on their legs or feet.
**https://bugguide.net/node/view/217136/bgpage
====Courtship====
*Some Taeniapterinae are thought to wave their white-tipped front legs attract females.
**https://bugguide.net/node/view/217136/bgpage
*''Physiphora clausa'' appear to use leg-waving in courtship displays.
**https://www.flickr.com/photos/jean_hort/4663220062
*Waving of forelegs is included in the complex courtship behavior of ''Physiphora demandata''
**https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1439-0310.1979.tb00298.x
====Mimics for defense====
*Stilt-legged flies ''Rainieria antennaepes'' mimic ichneumonid wasps. They extend their fore-legs in front of their head, so they look like wasp antennae.
**https://thingsbiological.wordpress.com/2012/05/21/stilt-legged-flies-rainieria-antennaepes/ 
*Some hover-fly species mimic wasps by mock stinging, leg waving, or wing wagging.
**https://www.jstor.org/stable/10.1086/674612
*Wing-waving to mimic salticid spiders.
**https://www.researchgate.net/publication/27373081 https://www.researchgate.net/publication/6083895&lt;br&gt;
&lt;br&gt;

===Number of iNat records in Acalyptrate fly families===
The [[w:acalyptratae|acalyptrate fly clade]] includes the following superfamilies and families:&lt;br&gt;

* '''Carnoidea'''
** Acartophthalmidae         0
** Australimyzidae           0
** Braulidae (bee lice)         1
** Canacidae (beach flies)         3
** Carnidae (bird flies)         0
** Chloropidae (frit flies)         259
** Cryptochetidae              1
** Inbiomyiidae                0
** Milichiidae (freeloader flies) 158
&lt;br&gt;
* '''Diopsoidea'''
** Diopsidae (stalk-eyed flies)    545
** Gobryidae                   0
** Megamerinidae               0
** Nothybidae                   0
** Psilidae (rust flies)         29
** Somatiidae                   0
** Syringogastridae            0
&lt;br&gt;
* '''Ephydroidea'''
** Camillidae  0
** Campichoetidae   0
** Curtonotidae (quasimodo flies)   15
** Diastatidae 0
** Drosophilidae (vinegar and fruit flies) 312
** Ephydridae (shore flies) 117
&lt;br&gt;
* '''Lauxanioidea'''
** Celyphidae (beetle flies)  0
** Chamaemyiidae (aphid flies)  24
** Cremifaniidae  0
** Lauxaniidae (lauxaniid flies)  710
&lt;br&gt;
* '''Nerioidea'''
** Cypselosomatidae  0
** Fergusoninidae  0
** Micropezidae (stilt-legged flies)  245
** Neriidae  109
** Strongylophthalmyiidae  0
** Tanypezidae (stretched-foot flies)  0
&lt;br&gt;
* '''Opomyzoidea'''
** Agromyzidae (leaf-miner flies) 161
** Anthomyzidae  3
** Asteiidae  4
** Aulacigastridae  2
** Clusiidae (druid flies) 2
** Marginidae  0
** Neminidae 0 
** Neurochaetidae 0
** Odiniidae  0
** Opomyzidae  4
** Periscelididae  1
** Teratomyzidae  0
** Xenasteiidae  0
&lt;br&gt;
* '''Sciomyzoidea''' 
** Coelopidae (kelp flies)  51
** Conopidae (thick-headed flies)  192
** Dryomyzidae  1
** Helcomyzidae  0
** Helosciomyzidae  0
** Heterocheilidae  0
** Huttoninidae  0
** Natalimyzidae  0
** Phaeomyiidae  0
** Ropalomeridae  1
** Sciomyzidae (marsh flies)  67
** Sepsidae (black scavenger flies)  269
&lt;br&gt;
* '''Sphaeroceroidea'''
** Chyromyidae (golden flies)  19
** Heleomyzidae (heleomyzid flies)  151
** Nannodastiidae  0
** Sphaeroceridae (lesser dung flies)  48
&lt;br&gt;
* '''Tephritoidea'''
** Ctenostylidae  1
** Lonchaeidae (lance flies) 47
** Pallopteridae (flutter-wing flies)  5
** Piophilidae (cheese skipper flies) 1
** Platystomatidae (signal flies)  683
** Pyrgotidae (scarab-pursuing flies)  119
** Richardiidae  0
** Tachiniscidae  2
** Tephritidae (fruit flies)  1,759
** Ulidiidae (picture-winged flies) 165

== References ==</text>
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See also [[Universal Bibliography/Bibliography|Bibliography]]

This part of the [[Universal Bibliography]] is a bibliography of literature.

See [[s:Category:Literature]], [[s:Category:History of literature]], [[w:Bibliography of encyclopedias: literature]] and [[w:Category:Works about literature]]

==World==
*Cassell's Encyclopaedia of World Literature. 1953. 2nd Ed: 1973. vol 1 (histories and general articles): [https://books.google.co.uk/books?id=soIYAAAAIAAJ]. vol 3: [https://books.google.co.uk/books?id=AIEYAAAAIAAJ]. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&amp;pg=PA197#v=onepage&amp;q&amp;f=false].

*Damrosch. What is World Literature? 2003. [https://books.google.co.uk/books?id=yY-17mtp9R8C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Series:
*Edmund Gosse (ed). Literatures of the World. D Appleton and Co [https://en.m.wikisource.org/wiki/Page:A_history_of_Bohemian_literature.pdf/444]

==English==
*Bateson. Cambridge Bibliography of English Literature. 1940. Watson, Supplement 1957.
*Concise Cambridge Bibliography of English Literature
*New Cambridge Bibliography of English Literature
*Annual Bibliography of English Language and Literature. Cambridge University
*Ewen. Bibliography of Eighteenth Century English Literature. Columbia University. 1935
*Marcuse. A Reference Guide for English Studies. University of Calfornia. 1990
*Bracken. Reference Works in British and American Literature. Libraries Unlimited. 1998
*Kennedy and Sands. A Concise Bibliography for Students of English. Stanford University
*Pelican Guide to English Literature
*[[w:The Cambridge History of English and American Literature|Cambridge History of English and American Literature]]
*[[s:The Cambridge History of English Literature|Cambridge History of English Literature]]
*Concise Cambridge History of English Literature
*New Cambridge History of English Literature
*Oxford History of English Literature
*Oxford Illustrated History of English Literature
*Short Oxford History of English Literature
*Routledge History of Literature in English
*Cambridge History of Early Medieval English Literature
*Cambridge History of Medieval English Literature
*Cambridge History of Early Modern English Literature
*Cambridge History of Victorian Literature
*Cambridge History of Twentieth Century English Literature
*[[s:The Cambridge History of American Literature|Cambridge History of American Literature]]

Periodicals
*Liverpool Magazine (1890)
*Literary Garner (1835)

===United States===
See [[w:Category:American literature by state]]
*Dershem. An Outline of American State Literature. 1921

Arizona:
*Joseph Amasa Munk, History of Arizona Literature, 1925
*Mary G Boyer, Arizona in Literature, 1935
*Etulain, &quot;Contours of Culture in Arizona and the Modern West&quot; in Luey and Stowe, Arizona at  Seventy-five, 1987
*Diaz, &quot;A Bibliography of Bibliographies Relating to the History and Literature of Arizona and New Mexico&quot; (1958) 14 Arizona Quarterly 197

Colorado:
*Eugene Parsons, &quot;Colorado Literature&quot; in Stone, History of Colorado, 1918, volume 1, chapter 42, p 877 [https://books.google.co.uk/books?id=-uVYAAAAMAAJ]
*Levette J Davidson, &quot;The Literature of Colorado&quot; in Hafen. Colorado and Its People: A Narrative and Topical History of the Centennial State. Volume 2. Chapter 8. Page 225 [https://books.google.co.uk/books?id=sncXAAAAIAAJ]
*Fritz. &quot;Literature&quot;. Colorado, the Centennial State. 1941. p 417 [https://books.google.co.uk/books?id=EU0UAAAAYAAJ]
*&quot;Books and Writers&quot;. Colorado, a Guide to the Highest State. 1941. p 96 [https://books.google.co.uk/books?id=3o8GAQAAIAAJ]
*Eugene Parsons, &quot;The Study of Colorado Literature&quot; (1918) Colorado School Journal, vols 34-35, p 24 [https://books.google.co.uk/books?id=QxNRAQAAMAAJ]
*&quot;A Plea for the Study of Colorado Literature&quot; (1918) The Trail: A Magazine &quot;for Colorado&quot;, vol 11, p 12 [https://books.google.co.uk/books?id=K7QTAAAAYAAJ]

Oregon:
*Powers, Alfred. History of Oregon Literature. Metropolitan Press. 1935 [https://books.google.co.uk/books?id=JzELAAAAMAAJ]
*Horner, John B. Oregon Literature. 1899 [https://books.google.co.uk/books?id=3ecWSpoFMcQC&amp;pg=PA1#v=onepage&amp;q&amp;f=false]

==French==
See [[s:Category:French literature]]

Bibliographies and bibliographical works:
*A Critical Bibliography of French Literature. Syracuse University Press. [https://books.google.co.uk/books?id=IFJQl7eUrg4C&amp;pg=PR3#v=onepage&amp;q&amp;f=false vol 5]
*Bassan, Breed and Spinelli. An Annotated Bibliography of French Language and Literature. 2nd Ed: 1976 [https://books.google.co.uk/books?id=BdkaAAAAMAAJ]
*French XX Bibliography: A Bibliography for the Study of French Literature and Culture since 1885. [https://books.google.co.uk/books?id=VxVxFxyDOmkC&amp;pg=PA19125#v=onepage&amp;q&amp;f=false]
*Foulet. A Bibliography of Medieval French Literature for College Libraries. 1915 [https://books.google.co.uk/books?id=httNAQAAIAAJ]
*Kirsop. The Bibliography of French Literary History: Progress, Problems, Projects. 1964. [https://books.google.co.uk/books?id=Xt7nAAAAMAAJ]

*Jaffe. Bibliography of French Literature in American Magazines in the 18th Century. Michigan State College Press. 1951. [https://books.google.co.uk/books?id=Cy7GGsr1NI8C]
*Raimbert. French Literature in Mauritius (1800-1979): A Select Bibliography in the City Library of Port Louis. 1980 [https://books.google.co.uk/books?id=eQYpAQAAIAAJ]
*French Literature in Early American Translation: A Bibliographical Survey of Books and Pamphlets Printed in the United States from 1668 Through 1820. 1977. [https://books.google.co.uk/books?id=CYI0AQAAIAAJ]

History:
*Cambridge History of French Literature
*Coward. A History of French Literature: From Chanson de geste to Cinema. 2002. Paperback 2004. [https://books.google.co.uk/books?id=K8uS9vLpwuYC&amp;lpg=PP1&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Hollier. A New History of French Literature. 1989. 1994. [https://books.google.co.uk/books?id=nGQOodBVG9YC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Cazamian. A History of French Literature. Clarendon Press.1955. Reprinted 1967. [https://books.google.co.uk/books?id=W5PwAAAAMAAJ]
*Nitze and Dargan. A History of French Literature: From the Earliest Times to the Present. 1930. [https://books.google.co.uk/books?id=QT0nAAAAMAAJ]
*Butler. A History of French Literature. 1923. Reissued 1966. [https://books.google.co.uk/books?id=sPAoAAAAYAAJ]
*Dowden. A History of French Literature. (Literatures of the World). 1900 [https://books.google.co.uk/books?id=XWdcAAAAMAAJ]
*Wright. A History of French Literature. (Oxford French series). [https://books.google.co.uk/books?id=_O0oAAAAYAAJ]
*Schwarz. An Outline History of French Literature. 1924. 1932. [https://books.google.co.uk/books?id=9_fnAAAAMAAJ]
*Demogeot. History of French Literature. Adapted from the French by Bridge. 1874. [https://books.google.co.uk/books?id=LgxONYxlEogC&amp;pg=PP9#v=onepage&amp;q&amp;f=false]

*Brunetière. Manual of the History of French Literature. 1898. [https://books.google.co.uk/books?id=WOHnAAAAMAAJ]

*Brereton. A Short History of French Literature. 1954. 2nd Ed:1976. [https://books.google.co.uk/books?id=DegoAAAAYAAJ]
*Bisson. A Short History of French Literature: From the Middle Ages to the Present Day. 1943. [https://books.google.co.uk/books?id=TLQywgEACAAJ]
*Hudson and Jack. A Short History of French Literature. 1919 [https://books.google.co.uk/books?id=8xIPAAAAQAAJ]
*Saintsbury. A Short History of French Literature. 1882. 2nd Ed: 1884. 7th Ed: 1917 [https://books.google.co.uk/books?id=WDoTAAAAMAAJ] [https://books.google.co.uk/books?id=AWFcAAAAMAAJ]

*Finch. French Literature: A Cultural History. 2010. [https://books.google.co.uk/books?id=8L0Z8uYUWj0C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

*Prendergast. History of Modern French Literature: From the Sixteenth Century to the Twentieth Century. 2017. [https://books.google.co.uk/books?id=2QtpDQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Laun. History of French Literature: From the Classical Renaissance until the End of the Reign of Louis XIV. 1883. [https://books.google.co.uk/books?id=bdZEAQAAIAAJ]

*Farrant. Introduction to Nineteenth-Century French Literature. 2007. [https://books.google.co.uk/books?id=m4HjBAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Vinet. History of French Literature in the Eighteenth Century. Translated by Bryce. 1854. [https://books.google.co.uk/books?id=5M803wEuBswC&amp;pg=PR1#v=onepage&amp;q&amp;f=false]

*Jacqueline Cerquiglini-Toulet. A New History of Medieval French Literature. Translated by Sara Preisig. 2011. [https://books.google.co.uk/books?id=h42MQw6TfAcC&amp;pg=PT3#v=onepage&amp;q&amp;f=false]

*Konta. The History of French Literature: From the Oath of Strasburg to Chanticler. 1914. [https://books.google.co.uk/books?id=g2FcAAAAMAAJ]

*Cambridge Companion to Medieval French Literature

*Holmes. A History of Old French Literature: From the origins to 1300. 1938. Revised Ed: 1962. [https://books.google.co.uk/books?id=0UxcAAAAMAAJ]

*Sainstbury. A History of the French Novel (to the Close of the 19th Century). 1919. [https://books.google.co.uk/books?id=GAxJAQAAIAAJ]

==Japanese==
*Ryōzō Matsumoto. Japanese Literature New and Old. Hokuseido Press. 1966. [https://books.google.co.uk/books?id=EzftWTtGXzgC]
*J Ingram Bryan. The Literature of Japan. 1929. Kennikat Press. Port Washington. Reissued 1970. [https://books.google.co.uk/books?id=BwazAAAAIAAJ]
*Clay MacCauley. Japanese Literature. 1898. [https://books.google.co.uk/books?id=9nYuAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Epiphanius Wilson. Japanese Literature: Including Selections from Genji Monogatari and Classical Poetry and Drama of Japan. 1900. [https://books.google.co.uk/books?id=Iy4NAAAAYAAJ&amp;pg=PP7#v=onepage&amp;q&amp;f=false]
*Katsuhiko Takeda. Essays on Japanese Literature. Waseda University Press. 1977. [https://books.google.co.uk/books?id=VKkPAAAAYAAJ]
*Suzuki Sadami. The Concept of &quot;Literature&quot; in Japan. International Research Center for Japanese Studies. Kyoto. 2006. [https://books.google.co.uk/books?id=DMQ_AQAAIAAJ]

Bibliography
*Modern Japanese Literature in Western Translations: A Bibliography. International House of Japan Library. [https://books.google.co.uk/books?id=WZ7QAAAAMAAJ]

Periodicals
*Japanese Literature Today [https://books.google.co.uk/books?id=NyYHAQAAIAAJ]
*[[w:Proceedings of the Association for Japanese Literary Studies|Proceedings of the Association for Japanese Literary Studies]]

Kokubungaku and nihonbungaku
*Tomoko Aoyama. &quot;From national literature to multicultural literature in Japanese language&quot;. Kaori Okano and Yoshio Sugimoto (eds). Rethinking Japanese Studies: Eurocentrism and the Asia-Pacific Region. Routledge Contemporary Japan Series. Chapter 4. pp [https://books.google.co.uk/books?id=sEcrDwAAQBAJ&amp;pg=PA53#v=onepage&amp;q&amp;f=false 53] to 72.

Reviewed
*Donald Richie. Japanese Literature Reviewed. 2003. [https://books.google.co.uk/books?id=ejJmAAAAMAAJ]

History
*Shuichi Kato. A History of Japanese Literature: From the Man'yōshū to Modern Times. New Abridged Edition. Japan Library. 1997. [https://books.google.co.uk/books?id=wUxOuD0NS5kC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Edward Putzar. Japanese Literature: A Historical Outline. University of Arizona Press. [https://books.google.co.uk/books?id=2kiBAAAAIAAJ]
*W G Aston. A History of Japanese Literature. (Literatures of the World). 1903. [https://books.google.co.uk/books?id=T4EMAAAAYAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Naomi Fukuda (ed). Literature. (Japanese History: A Guide to Survey Histories, Part 2). Center for Japanese Studies, University of Michigan. 1984. [https://books.google.co.uk/books?id=QsoUAQAAIAAJ]

Today
*A Survey of Japanese Literature Today. Japan P.E.N. Club. 1984. [https://books.google.co.uk/books?id=OcFDAQAAIAAJ]

Contemporary
*Kokusai Bunka Shinkokai (Japan Cultural Society). Introduction to Contemporary Japanese Literature: Synopese of Major Works: 1956-1970. University of Tokyo Press. 1972. [https://books.google.co.uk/books?id=XPQkHx6wR4IC]

Modern
*A Classified Catalogue of Modern Japanese Literature (Meiji, Taisho, Showa). University of Washington Library. 1964. [https://books.google.co.uk/books?id=lD8XAQAAMAAJ]
*Routledge Handbook of Modern Japanese Literature. 2016. [https://books.google.co.uk/books?id=EMpJDAAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*J Thomas Rimer and Van C Gessel (eds). The Columbia Anthology of Modern Japanese Literature. 2007. vol 2. [https://books.google.co.uk/books?id=BAg9tUJR1aEC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
**Abridged. 2011. [https://books.google.co.uk/books?id=VrEYtVFv67oC&amp;pg=PP1#v=onepage&amp;q&amp;f=false vol 1].
*Karatani Kōjin. Origins of Modern Japanese Literature. 1993. [https://books.google.co.uk/books?id=hPJO2vEQgjYC&amp;pg=PP1#v=onepage&amp;q&amp;f=false] 
*Kan Kikuchi. History and Trends of Modern Japanese Literature. Tokyo. 1936. [https://books.google.co.uk/books?id=TU4DAAAAMAAJ]
*Edward Mack. Manufacturing Modern Japanese Literature: Publishing, Prizes, and the Ascription of Literary Value. [https://books.google.co.uk/books?id=WnDI6s9surUC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Donald Keene (ed). Modern Japanese Literature: From 1868 to the Present Day. Grove Press. 1956. [https://books.google.co.uk/books?id=5yxkAAAAMAAJ]
*Saeki Shōichi. Hidden Dimensions in Modern Japanese Literature. The Japan Foundation, Office for the Japanese Studies Center. [https://books.google.co.uk/books?id=OCYHAQAAIAAJ]

20th century and Showa era
*[https://www.nippon.com/en/series/c152/ Japanese Literature in the Twentieth Century: A Shōwa Retrospective]. Nippon.com
**[https://www.nippon.com/en/japan-topics/c15201/ Writing in the Shadow of Oppression: Japanese Books from 1926 to 1944]
**[https://www.nippon.com/en/japan-topics/c15202/ Shaped by Conflict: Japanese Literature After World War II]
**[https://www.nippon.com/en/japan-topics/c15203/ Seeking New Values in an Age of Growth: Japanese Books from 1955 to 1964]
**[https://www.nippon.com/en/japan-topics/c15204/ Historical Fiction and Social Issues: Japanese Books from 1965 to 1974]
**[https://www.nippon.com/en/japan-topics/c15205/ The Rise of Popular Fiction: Japanese Books in the 1970s and 1980s]

Meiji and Taisho
*Kimura Ki (editor and compiler). Japanese Literature: Manners and Customs in the Meiji-Taishó Era. Ōbunsha. [https://books.google.co.uk/books?id=rBQrAAAAIAAJ]

Early modern
*Haruo Shirane (ed). Early Modern Japanese Literature: An Anthology, 1600-1900. Abridged Edition. 2008. [https://books.google.co.uk/books?id=SN72QCVBpVAC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Classical
*The Princeton Companion to Classical Japanese Literature [https://books.google.co.uk/books?id=BSmMbQhafJoC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Introduction to Classic Japanese Literature. Kokusai Bunka Shinkokai. 1948. [https://books.google.co.uk/books?id=WJAPAAAAYAAJ]

Traditional
*Haruo Shirane (ed). Traditional Japanese Literature: An Anthology, Beginnings to 1600. 2007. [https://books.google.co.uk/books?id=LsHfIsIXgEgC&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Literary criticism; Literary studies
*Seth Jacobowitz and Jonathan E Abel (eds). Modern Japanese Literary Studies. 2026. [https://books.google.co.uk/books?id=s-_AEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Studies in Modern Japanese Literature: Essays and Translations in Honor of Edwin McClellan. 1997. [https://books.google.co.uk/books?id=_5EPAAAAYAAJ]

Anthology
*Donald Keene. Anthology of Japanese Literature from the earliest era to the mid-nineteenth century. Grove Press. 1955. [https://books.google.co.uk/books?id=9h8tAAAAMAAJ] Great Britain. 1956. [https://books.google.co.uk/books?id=LCxkAAAAMAAJ]. Evergreen Ed: 1960. [https://books.google.co.uk/books?id=rumBAAAAIAAJ]

Novels

Modern novels
*Nancy Junko Beauchamp. Modern Japanese Novels in English: A Selected Bibliography. Service Center for Teachers of Asian Studies, Association for Asian Studies, Ohio State University. May 1974. [https://books.google.co.uk/books?id=WltEAAAAIAAJ]
*Kinya Tsuruta and Thomas E Swann (eds). Approaches to the Modern Japanese Novel. Sophia University. Tokyo. 1976. [https://books.google.co.uk/books?id=bhdkAAAAMAAJ]

Short stories
*Theodore W Goossen. The Oxford Book of Japanese Short Stories. 1997. Reissued 2002. [https://books.google.co.uk/books?id=VWfJkFfyBn0C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]

Modern short stories
*Thomas E Swann and Kinya Tsuruta (eds). Approaches to the Modern Japanese Short Story. Waseda University Press. 1982. [https://books.google.co.uk/books?id=IJYPAAAAYAAJ]

Poetry
*&quot;Japan, Poetry of&quot;. The Princeton Encyclopedia of Poetry and Poetics. 4th Ed. [https://books.google.co.uk/books?id=uKiC6IeFR2UC&amp;&amp;pg=PA754#v=onepage&amp;q&amp;f=false p 754]. See also articles &quot;Japan, Modern Poetry of&quot; and &quot;Japanese Poetics&quot;. 
*J Thomas Rimer and Robert E Morrell. Guide to Japanese Poetry. 1975: [https://books.google.co.uk/books?id=EysyAAAAMAAJ]. 2nd Ed: 1984: [https://books.google.co.uk/books?id=BPEaAAAAMAAJ].
*Yone Noguchi. The Spirit of Japanese Poetry. [https://books.google.co.uk/books?id=5K8PAAAAYAAJ]
*Miyamori Asatarō. Masterpieces of Japanese Poetry Ancient and Modern.  [https://books.google.co.uk/books?id=hnAmAQAAIAAJ]
*Dean Anthony Brink. Japanese Poetry and its Publics: From Colonial Taiwan to Fukushima. [https://books.google.co.uk/books?id=IUk4DwAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Curtis Hidden Page. Japanese Poetry: An Historical Essay with Two Hundred and Thirty Translations. 1923. [https://books.google.co.uk/books?id=rqEPAAAAYAAJ]
*Thomas Fitzsimmons. Japanese Poetry Now. Schocken Books. 1972. [https://books.google.co.uk/books?id=TQ4QAAAAYAAJ]
*Leith Morton. An Anthology of Contemporary Japanese Poetry. Garland Publishing. 1993. [https://books.google.co.uk/books?id=0OwPAAAAYAAJ]
*Leith Morton. Avant-Garde Japanese Poetry and Poetics: Contemporary Poetry Handbook, 2000–2021. 2026. [https://books.google.co.uk/books?id=7obXEQAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Leith Morton. Modernism in Practice: An Introduction to Postwar Japanese Poetry. 2004. [https://books.google.co.uk/books?id=3N5G6WvGLi0C&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Harry and Lynn Guest and Kajima Shozo. Post-war Japanese Poetry. 1972. Penguin Books. [https://books.google.co.uk/books?id=5QoQAAAAYAAJ] 
*Alexander Dolin. The Silver Age of Japanese Poetry: Romanticism and Symbolism. Akita International University Press. 2010. [https://books.google.co.uk/books?id=0IdT0XOoLeoC]
*Steven D Carter. Traditional Japanese Poetry: An Anthology. Stanford University Press. [https://books.google.co.uk/books?id=dq7TOrkTCP0C&amp;pg=PP3#v=onepage&amp;q&amp;f=false]
*Basil Hall Chamberlain. The Classical Poetry of the Japanese. 1880. [https://books.google.co.uk/books?id=-HUuAAAAYAAJ&amp;pg=PR3#v=onepage&amp;q&amp;f=false]
*Douglas Kenning. The Romanticism of 17th Century Japanese Poetry. 1998. [https://books.google.co.uk/books?id=1fcZAQAAIAAJ]
*Robert H Brower and Earl Miner. Japanese Court Poetry. The Cresset Press. Great Britain. 1962. [https://books.google.co.uk/books?id=Fztgn3lHX8UC]

Modern poetry
*A R Davis (ed). Modern Japanese Poetry. University of Queensland Press. 1978. The Open University Press. Milton Keynes. 1979. [https://books.google.co.uk/books?id=v0aBAAAAIAAJ]
*Edith Marcombe Shiffert and Yuki Sawa. Anthology of Modern Japanese Poetry. 1972. [https://books.google.co.uk/books?id=OTDRAgAAQBAJ&amp;pg=PP1#v=onepage&amp;q&amp;f=false]
*Ichiro Kono and Rikutaro Fukuda. An Anthology of Modern Japanese Poetry. Kenkyusha. Tokyo. 1957. [https://books.google.co.uk/books?id=ZDpkAAAAMAAJ]

Books
*[https://www.tokyoweekender.com/art_and_culture/books-and-literature/translated-japanese-fiction-fall-2026/ 8 Japanese Books To Curl Up With This Fall]. Tokyo Weekender. 16 September 2026.

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You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:17, 2 June 2021 (UTC)&lt;/div&gt;
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    <title>Motivation and emotion/Wikiversity/Figures</title>
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      <contributor>
        <username>Jtneill</username>
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      <comment>/* Customise figure presentation */ Expand and clarify</comment>
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      <text bytes="7489" sha1="6pdpiom46yh00amz0doj7vo2t21bq1o" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|200px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|200px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|200px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

'''Figures''' can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Creating media==
Creating media is sometimes the best way to illustrate psychological concepts because it allows you to tailor the content to the topic. Original media uploaded to Wikimedia Commons allows others to use, which is a [[Motivation and emotion/Assessment/Social contribution|social contribution]].

You can create your own media by:
* Taking photographs
* Drawing diagrams, models, flowcharts, timelines, or concept maps
* Creating graphs, charts, or infographics based on research findings
* Recording audio (e.g., pronunciations, interviews, or narrated explanations)
* Creating videos, animations, or screencasts
* Using the [[c:Commons Lab/Illustration workshop|Commons Graphic Lab]] to request assistance with improving or creating images
* Using [[c:Commons media|artificial intelligence tools]] where appropriate and in accordance with Wikimedia Commons policies

Student-created diagrams are particularly valuable because they can:
* Simplify complex psychological theories and research
* Visually represent relationships between concepts
* Improve reader understanding and engagement
* Demonstrate your own interpretation and synthesis of the literature

When creating media:
* Aim for accuracy, clarity, and simplicity
* Use readable text and labels
* Ensure that colours, symbols, and formatting enhance understanding
* Create media that can be understood independently of the surrounding text
* Consider accessibility (e.g., colour contrast, descriptive captions, and alternative text)

Before creating new media, check whether suitable material already exists on Wikimedia Commons.

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Start with '''Figure #'''. 
** Describe and connect the image to key point(s) made in the main text
** There is no need to provide additional acknowledgement about the image source because this meta-data is available by clicking on the image
* Citation
** Each figure must be explicitly cited in text at least once (e.g., see Figure 1)
* Integration
** Figures should directly support the argument or explanation in adjacent text, rather than being unintegrated adornments

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
&lt;noinclude&gt;
[[Category:Motivation and emotion/Wikiversity]]
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  <page>
    <title>Playing</title>
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      <comment>==Discussion questions, essay ideas, and learning related AI prompt ideas== * For adults, how can being productive feel like play?  * What are aspects of modern life that prevent or hinder adults being productive members of society from being a playful activity?</comment>
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      <text bytes="9822" sha1="9xjht73e5jt2k5kc9turao5f9o0yd5s" xml:space="preserve">—Enjoyable Activity
[[File:Playing kula mbakishie baba by Rasheedhrasheed.jpg|thumb|Play is fun and instructive.]]
{{TOC right | limit|limit=2}} 
== Introduction ==
Skipping, jumping, dancing, singing, fiddling, exploring, imagining, pretending, fantasizing, joking, doodling, visiting, and just goofing off. This is fun, this is [[w:Play_(activity)|play]], this is OK.
== Objectives ==
The objectives of this course are to help students:
*Better understand the nature of play,
*Understand the purpose of play,
*Understand the benefits of play,
*Understand the boundaries of play, 
*Enjoy playing, and
*Use play to solve problems.

This course is part of the [[Wisdom/Curriculum|Applied Wisdom curriculum]].

This course draws heavily on the [https://emotionalcompetency.com/play.htm materials published previously]. We are grateful the author has placed that article into the public domain.

If you wish to contact the instructor, please [[Special:EmailUser/Lbeaumont|click here to send me an email]] or leave a comment or question on the [[Talk:Playing|discussion page]].

== Characterizing Play ==
For the purposes of this course, we describe [[w:Play_(activity)|play]] as:
*Pleasure without apparent purpose
*Activity for amusement or recreation

More [[w:Play_(activity)#Definitions|formal definitions]] are available.

== Related Terms ==
Synonyms for ''play'' include caper, dalliance, delight, diversion, foolery, frolic, fun, gambol, game, gaming, happiness, humor, jest, joking, lark, match, pastime, pleasure, prank, recreation, relaxation, romp, sport, sportiveness, and teasing. As we use it here it does not include any activities or behaviors that harm or exploit anyone.  
== Benefits ==
Although it appears purposeless, play has important long-term benefits. Play promotes brain development, creative thinking, and problem solving.  Play is an important catalyst for learning; it prepares us to deal effectively with new or unexpected situations. Experimenting with socialization as we play teaches us the rules and limits of acceptable and unacceptable social behavior through a wide variety of experiences in a relatively safe environment. Play increases [[Emotional Competency|emotional competence]]; it allows us to simulate a broad range of new experiences easily and safely as we learn from them quickly. Play helps us learn how the world works and how we can interact with it as we test the system in a variety of ways. Through play we learn the difference between acceptable and unacceptable risk taking. The rapid trial and error of play increases our creativity and innovation.

[[w:Learning_through_play|Learning through play]] has been long recognized as a critical aspect of childhood and child development.

Play can suspend or displace predatory behavior and overcome even a substantial differential in [[w:Power_(social_and_political)|power]]. Signals of playful intent are widely recognized. Stuart Brown states that the basis of human trust is established through play signals.&lt;ref&gt;{{cite book |last1=Brown |first1=Stuart |last2=Vaughan |first2=Christopher |date=February 11, 2009 |title=Play: How it Shapes the Brain, Opens the Imagination, and Invigorates the Soul |publisherAvery |pages=252 |isbn=}}&lt;/ref&gt;

Although often [[q:Plato#Misattributed|misattributed to Plato]], the observation “You can discover more about a person in an hour of play that in a year of conversation” remains insightful.

== Play is: ==
*done for its own sake; it has no apparent purpose or goal.
*voluntary; you choose to play simply because you want to. We play spontaneously. 
*inherently attractive; play is its own reward, you are intrinsically motivated to play simply because it is fun, exciting, and not boring.
*mentally engaging; attention is totally focused on the play activity. This has two rather pleasant consequences. You become unaware of time passing; you are set free from time and enjoy the experience of flow. Also, you are not self-conscious; you become unaware of yourself and are free from any pretenses.
*spontaneous and improvisational; no preparation or planning is needed. Chance ideas, objects, or events are readily incorporated. Play is exploration and discovery.
*alluring and seductive; it is something we want to continue doing.

Play often incorporates anticipation, curiosity, surprise, pleasure, and a new understanding that can lead to a new strength and a new level of play. 
== Play is OK ==
Play can provide many benefits, even within our work lives. For example, play:
*provides a sense of competence, connection, and purpose that increases our involvement, commitment to, and enjoyment of our work. Incorporating a sense of play into our work provides intrinsic motivation for the work. 
*increases our creativity as we play with crazy new ideas, follow hunches, and indulge fantasies, 
*increases skills mastery through experimentation, exploration, serendipity, involvement, attention, persistence, and practice.
*is important for strengthening our personal relationships and sustaining emotional intimacy.

Allow yourself the pure joy of play without feeling frivolous, embarrassed, or superficial. Integrate play into work so that you enjoy your work and increase your overall effectiveness.
== The Boundaries of Play ==
If we are careless or cruel play can sometimes degenerate into destructive activities: 
*if the allure of play, video games, or gambling for example becomes obsessive or [[w:Addiction|addictive]] it is no longer play.
*If the activity becomes sadistic or cruel, it is not play.
*If someone is domineering, aggressive, or violent they are not playing.

People sincerely care about the others they are playing with. Not all purposeless activities are play. 
Play is not:
*Harmful to anyone or anything,
*Avoiding, neglecting, or escaping your responsibilities,
*Taken so seriously that the fun disappears,
*A substitute for facing the demands of the real world.

Play is fun for all. If you are [[w:Fear|fearful]], [[w:Anxiety|anxious]], [[w:Suffering|hurt]], [[Earning Trust|distrustful]], [[w:Abuse|abusive]], or [[w:Mental_distress|distressed]], you are not playing.

== Many possibilities ==
Play can take many forms, such as [[w:Improvisation|improvisation]] or pretense, interactive, performance, mimicry, games, sports, and thrill-seeking.

Here are some possibilities:
*[[w:Role-playing|Role playing]], including [[w:Role-playing_game|role playing games]],
*[[w:Free_Play:_Improvisation_in_Life_and_Art|Free play]],
*Games chosen from this [[w:Category:Lists_of_games|list of games]],
*Sports chosen from this [[w:List_of_sports|list of sports]],
*[[w:Scenario_planning|Scenario planning]].
== Assignment ==
Find ways to solve problems by playing. For example:
*If you are stressed, find a playful way to relieve your stress.
*If you are at an impasse while working to solve a problem, find a playful way to introduce new ideas, chaos, new perspectives, or new people.
**Find playful ways to [[Unleashing_Creativity|unleash creativity]].
*If you are seeking new ideas, find playful ways to unleash your imagination.
**Use the [[Thinking Tools|thinking tools]].
*If you are learning some new skill, find playful ways to practice elements of that skill.
*If you are enduring drudgery, find playful ways to break up the monotony, overcome boredom, and become reinvigorated.
*If you are trapped in conflict, find some playful approach to [[Transcending Conflict|transcending conflict]]. 
*Find playful ways to strengthen relationships.

== Recommended Reading ==
Students wanting to learn more about playing may be interested in reading the following books: 

*{{cite book |last1=Brown |first1=Stuart |last2=Vaughan |first2=Christopher |date=February 11, 2009 |title=Play: How it Shapes the Brain, Opens the Imagination, and Invigorates the Soul |publisherAvery |pages=252 |isbn=}}

*{{cite book |last1=Iggulden |first1=Conn|last2=Iggulden |first2=Hal |date=April 24, 2012 |title=The Dangerous Book for Boys |publisher=William Morrow |pages=288 |isbn=978-0062208972}}

*{{cite book |last1=Robinson |first1=Ken|last2=Aronica |first2=Lou |date=December 1, 2008 |title=The Element: How Finding Your Passion Changes Everything |publisher=Penguin Books |pages=304 |isbn=}}
*{{cite book |last=Kashdan |first=Todd B.|date=April 10, 2009 |title=Curious?: Discover the Missing Ingredient to a Fulfilling Life |publisher=HarperCollins |pages=355 |isbn=}}
*{{cite book |last=Nguyen |first=C. Thi  |date=April 23, 2020 |title=Games: Agency As Art |publisher=Oxford University Press |pages=256|isbn=978-0190052089}}
*{{cite book |last=Ridley |first=Matt |author-link=w:Matt_Ridley |date=May 19, 2020 |title=How Innovation Works: And Why It Flourishes in Freedom |publisher=Harper |pages=416 |isbn=978-0062916594}}
*[http://www.ted.com/index.php/talks/stuart_brown_says_play_is_more_than_fun_it_s_vital.html Why play is vital—no matter your age], May 2008 TED talk by Stuart Brown.
*[http://www.ted.com/talks/gever_tulley_on_5_dangerous_things_for_kids.html Five dangerous things for kids], March 2007 TED talk by Gever Tulley

I have not yet read the following books, but they seem interesting and relevant. They are listed here to invite further research.
*''Free Play: Improvisation in Life and Art'', by  Stephen Nachmanovitch
*''The Playful Mind: How to Restore the Happiness We Experienced as Children'', by Paul Daniel

==Discussion questions, essay ideas, and learning related AI prompt ideas==
* For adults, how can being productive feel like play? 
* What are aspects of modern life that prevent or hinder adults being productive members of society from being a playful activity? 

== References ==
&lt;references/&gt;
[[Category:Life skills]]
[[Category:Applied Wisdom]]
[[Category:Creativity]]
[[Category:Peace studies]]
{{Possibilities}}</text>
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    <title>C language in plain view</title>
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      <comment>/* Applications */</comment>
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      <text bytes="9878" sha1="khxkmokz1drt71332goc1xio2tx6nxe" xml:space="preserve">=== Introduction ===
* Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]])
* Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]])
* Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]])

=== Handling Repetition ===
* Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]])
* Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]])

=== Handling a Big Work ===
* Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]])
* Functions &amp; Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]])
* Functions &amp; Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]])
* Functions &amp; Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]])

=== Handling Series of Data ===

==== Background ==== 
* Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]])
 
==== Basics ====
* Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]])
* Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]])
* Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]])
* Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]])

==== Examples ==== 
* Spreadsheet Example Programs
:: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]])
:: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]])
:: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]])
:: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]])

==== Applications ==== 
* Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20260918.pdf |A.pdf]])
* Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]])
* Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]])
* Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]])
* Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]])
* Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]])
* Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]])

=== Handling Various Kinds of Data ===
* Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]])
* Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]])
* Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]])
* Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]])

=== Handling Low Level Operations ===
* Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]])
* Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]])
* Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]])
* Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]])

=== Declarations ===
* Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]])
* Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]])
* Scope 


=== Class Notes ===

* TOC ([[Media:TOC.20171007.pdf |TOC.pdf]])
* Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library
* Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements
* Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers
* Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts
* Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops
* Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control
* Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions
* Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope
* Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion
* Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions
* Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications
* Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions
* Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications
* Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) 
* Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2)
* Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO
* Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions
* Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications
* Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum
* Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List 
* Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing
* Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing


&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;
See also https://cprogramex.wordpress.com/

== '''Old Materials '''==

until 201201
* Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]])
* Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]])
* Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]])
* Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]])
* Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]])
* Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]])
* Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]])
* Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]])
* Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]])
* Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]])
* Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]])
* Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]])
* Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]])
 
&lt;br&gt;

until 201107
* Intro.1.A ([[Media:Intro.1.A.pdf |pdf]])
* Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]])
* Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]])
* Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]])
* Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]])
* Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]])
* Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]])
* Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]])
* Array.1.A ([[Media:Array.1.A.pdf |pdf]])
* Type.1.A ([[Media:Type.1.A.pdf |pdf]])
* Structure.1.A ([[Media:Structure.1.A.pdf |pdf]])


go to [ [[C programming in plain view]] ]

[[Category:C programming language]]

&lt;/br&gt;</text>
      <sha1>khxkmokz1drt71332goc1xio2tx6nxe</sha1>
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  </page>
  <page>
    <title>Large language models</title>
    <ns>0</ns>
    <id>302417</id>
    <revision>
      <id>2833664</id>
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      <timestamp>2026-09-18T01:39:05Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>(Wikipedia Readings) added descriptions</comment>
      <origin>2833664</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="27310" sha1="3llg2ypd02nc6k7tccmb9h33mg0vzxw" xml:space="preserve">{{Short description|Machine learning models designed for natural language processing}}
[[File:LLM-logo.svg|thumb]]
Large language models (LLM's) are software programs that are also known as a form of &quot;artificial intelligence&quot; (AI); LLM's are specifically an aspect of generative AI. This wiki area is for learning, teaching, and research related to LLM's. 
{{RightTOC}}
[[Image:Multiple attention heads.png|right|280px|thumb|An illustration of multiple attention heads, each having its own criteria of relevance of other tokens for one of the tokens within the scope of a context window. (For the purpose of illustration, the context window consists of only one sentence.]]

==Sub-pages==
* [[Large language models/Context economy of agent runs]] — why the cost of a multi-step agent run is dominated by repeated input, how to measure a run without double counting, and a controlled experiment on session length.

==Discourse and ideas==
Here is discourse and ideas related to large language models. Perhaps once significantly developed/refined, some of these can have their own sub-page or become a unique learning resource. 
===Learning wikis as training data===
Unless laws change, Creative Commons content appears to be valid training data for LLM's. As LLM's progress and advance, more and more data can be utilized to training increasingly complex models. Learning wikis devoted to learning, teaching, and resource, that allow for original research and original content creation (related to learning, teaching, and research), can potentially be extremely valuable (in terms of educational value) for large language models. Perhaps in the future (if this does not already exist), large language models will be able to continuously be trained on, retain, and learn from new data and information. Perhaps in the future, an open source large language model could only be trained on Creative Commons data, and therefore, all generated content would also be licensed under Creative Commons. 

==Discussion questions==
Here are some learning and teaching oriented discussion questions related to large language models. Humans can use language and mental effort to explore these ideas collaboratively, or some of these could be used as prompts to see how an LLM might respond. 
* Would a large language model that is only trained on Creative Commons licensed data only be capable of generating responses to prompts that can also be rightly and correctly licensed under a Creative Commons license? 
* How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)? 
* What are some ethical considerations related to large language models that should be considered? 
* What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think? 
* How can large language models help to advance and accelerate technological automation in ways that will benefit all of humanity? 
* In what ways can large language models help programmers to code?
* Can music be thought of a language within the realm of large language models? 
* What is differentiable computing and how does differentiable computing relate to large language models? 
* How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? 

== Educational prompt ideas==
These are original prompt ideas regarding ways to learn about large language models, and also to explore using LLM's for learning, teaching, and research. Input these into your preferred LLM (without quotes) to see what results are generated. LLM's might produce interesting or useful answers in response to these prompts. Some of these prompts may be interesting or useful for discussions among and between humans. 

* &quot;Describe to me how large language models can be utilized for learning, teaching, and research. Do this in an about 200 word two paragraph mini essay. Explain it to me like I am a freshman in community college.&quot; 
* &quot;Give me a list of 12 ways that large language models can be utilized for learning, teaching, and research.&quot;
* &quot;How can LLM's be utilized to accelerate the pace of research and scientific discovery?&quot;
* &quot;What are some ethical considerations related to large language models that should be considered?&quot;
* &quot;What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think?&quot;
* &quot;What are some project ideas to integrate large language models in with humanoid robots, and/or other sorts of robots? Please give me 15 project ideas that can be relatively simple or extremely complex.&quot;
* &quot;Please search the Internet if possible. In what ways have university professors and academic researchers been using large language models in the last year? Please respond in list form.&quot;
* &quot;In what ways can large language models help programmers to code? Please provide me 8 examples and respond in list form.&quot;
* &quot;Can music be thought of a language within the realm of large language models?&quot;
* &quot;What is differentiable computing and how does differentiable computing relate to large language models?&quot;
* &quot;How can one fine tune an open source large language model?&quot;
* &quot;What are some popular state of the art open source large language models. Please search the internet as helpful and respond to me in list form.&quot;
* &quot;Please give me a list of important terminology that I should be aware of when working with and training open source large language models. Please be comprehensive. Please respond in list form. And please search the internet as helpful.&quot;
* &quot;What sort of hardware should I utilize to run the most competent open source large language models that I want to utilize for learning, teaching, and research? Please search the internet as helpful.&quot;
* &quot;How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? Please respond in list form.&quot;
* &quot;How can researchers utilize large language models to create theories, hypothesis, and to formulate potential research studies? Please respond in short paragraphs, but in list form.&quot;

== Readings and learning media ==
=== Wikipedia ===
{{:Cross-domain_AI_topics}}
==== LLM Topics ====
Categories and lists:
: {{wc|Natural language processing}}
:: {{wc|Tasks of natural language processing}}
: {{wc|Large language models}}
:: {{wc|Generative pre-trained transformers}}
:: {{w|List of large language models}}

===== Basics (Wikipedia Readings) =====
: {{w|ChatGPT}}
: {{w|Large language model}}
: {{w|Prompt engineering}}
: {{w|GPT-4}}
: {{w|ChatGPT in education}}
: {{w|Turing test}}
: {{w|Natural-language understanding}}
: {{w|Word embedding}}
===== Intermediate (Wikipedia Readings) =====
: {{w|Transformer (deep learning architecture)}}
: {{w|Attention (machine learning)}}
: {{w|LLaMA}}
: {{w|Mistral AI}}
: {{w|Foundation model}}
: {{w|LangChain}}
: {{w|Generative pre-trained transformer}} (GPT)
: {{w|GitHub Copilot}}

===== Advanced (Wikipedia Readings) =====
: {{w|Reflection (artificial intelligence)}}
: {{w|Reasoning language model}}
: {{w|Retrieval-augmented generation}}
: {{w|Knowledge distillation}}
: {{w|Model compression}}
: {{w|History of natural language processing}}
: {{w|Neural scaling law}}
: {{w|GitHub Copilot}}
: {{w|Automated reasoning}}
: {{w|Mixture of experts}}
: {{w|Gemini (language model)}}
: {{w|Auto-GPT}}
: {{w|VideoPoet}}
: {{w|Artificial intelligence in Wikimedia projects}}
: {{w|Artificial intelligence content detection}}
: {{w|Language model}}
:: {{w|Language model benchmark}}
:: {{w|Language_model#Evaluation_and_benchmarks|Evaluation and benchmarks}}
::: {{w|MMLU}}
: {{wc|Tasks of natural language processing}}
:: {{w|Question answering}}
:: {{w|Sentiment analysis}}
:: {{w|Named-entity recognition}}
: {{w|Zero-shot learning}}
: More
:: Internals
::: {{w|Word2vec}}
::: {{w|Seq2seq}}
::: {{w|GloVe}}
:: {{w|List of large language models}}
::: {{w|BERT (language model)|BERT}}
::: {{w|T5 (language model)|T5}}
::: {{w|Llama (language model)|Llama}}
::: {{w|Chinchilla (language model)|Chinchilla AI}}
::: {{w|PaLM}}
::: {{w|Generative pre-trained transformer|GPT}}
::: {{w|GPT-1|1}}, {{w|GPT-2|2}}, {{w|GPT-3|3}}, {{w|GPT-J|J}}
:::: {{w|ChatGPT}}
:::: {{w|GPT-4|4}}, {{w|GPT-4o|4o}}
:::: {{w|OpenAI o1|o1}}, {{w|OpenAI o3|o3}}
::: {{w|Claude (language model)|Claude}}
::: {{w|Gemini (language model)|Gemini}}
:::: {{w|Gemini (chatbot)|chatbot}}
::: {{w|Grok (chatbot)|Grok}}
:: {{w|LaMDA}}
::: {{w|BLOOM (language model)|BLOOM}}
::: {{w|Project Debater}}
::: {{w|IBM Watson}}
::: {{w|IBM Watsonx}}
::: {{w|IBM Granite|Granite}}
::: {{w|Huawei PanGu|PanGu-Σ}}
::: {{w|DeepSeek}}
::: {{w|Qwen}}

===External===
: [https://arena-chapter1-transformer-interp.streamlit.app/ Transformer Interpretability, ARENA]
: [https://rdi.berkeley.edu/llm-agents/f24 LLM agents course, Berkeley], [https://www.youtube.com/watch?v=QL-FS_Zcmyo @youtube]
: https://anthropic.skilljar.com/
: https://hf.co/learn/, [https://hf.co/learn/smol-course Smol LLM fine-tuning course]
: https://academy.openai.com/
: https://cookbook.openai.com/
: https://academy.langchain.com/
: [https://medium.com/@tom_21755/understanding-causal-llms-masked-llm-s-and-seq2seq-a-guide-to-language-model-training-d4457bbd07fa Understanding Causal LLM’s, Masked LLM’s, and Seq2Seq: A Guide to Language Model Training Approaches]
: Docs
:: https://docs.x.ai/
:: https://platform.deepseek.com/
:: https://platform.openai.com/
:: https://docs.anthropic.com/
:: https://docs.mistral.ai/
: Papers, publications
:: https://huggingface.co/papers
:: [https://arxiv.org/abs/2201.11903 Chain-of-Thought Prompting Elicits Reasoning in Large Language Models, 2022]
:: [https://arxiv.org/abs/2106.09685 LoRA: Low-Rank Adaptation of Large Language Models, 2021]
:: [https://arxiv.org/abs/1706.03762 Attention Is All You Need, 2017]
: Articles
:: https://www.pinecone.io/learn/retrieval-augmented-generation/
:: [https://stpp.fordschool.umich.edu/tags/large-language-models Large Language Models] - Articles
:: [https://hai.stanford.edu/news/how-large-language-models-will-transform-science-society-and-ai How Large Language Models Will Transform Science, Society, and AI]
:: [https://insights.sei.cmu.edu/blog/harnessing-the-power-of-large-language-models-for-economic-and-social-good-foundations/ Harnessing the Power of Large Language Models For Economic and Social Good: Foundations]
:: [https://courses.grainger.illinois.edu/CS447/sp2023/Slides/Lecture27.pdf Lecture 27: Intro to Large Language Models]

==== Deep Reinforcement Learning ====
: [https://hf.co/learn/deep-rl-course/unit0/introduction Deep RL]
:: Huggy, Q-Learning

==== Model Context Protocol (MCP) Course ====
: [https://huggingface.co/learn/mcp-course/unit0/introduction MCP Course]
:: Continue, Gradio, Hugging Face Hub, Claude Code, GitHub, Slack

==== AI Agents Course ====
[https://hf.co/learn/agents-course/unit0/introduction Hugging Face AI Agents Course]
: [https://hf.co/learn/agents-course/unit1/introduction Introduction to Agents]
:: [https://huggingface.co/learn/agents-course/unit1/agent-steps-and-structure Thought-Action-Observation Cycle]
: [https://hf.co/learn/agents-course/unit2/introduction Frameworks for AI Agents]
:: [https://hf.co/learn/agents-course/unit2/smolagents/introduction smolagents] 
::: [https://huggingface.co/learn/agents-course/unit2/smolagents/code_agents code agents]
::: [https://huggingface.co/learn/agents-course/unit2/smolagents/tools tools]
::: [https://huggingface.co/learn/agents-course/unit2/smolagents/multi_agent_systems multi-agent]
::: ... [https://huggingface.co/docs/smolagents/index docs]
:: [https://hf.co/learn/agents-course/unit2/llama-index/introduction LlamaIndex]
::: ... [https://docs.llamaindex.ai/en/stable/understanding/ docs]
:: [https://hf.co/learn/agents-course/unit2/langgraph/introduction LangGraph]
::: ... [https://academy.langchain.com/courses/intro-to-langgraph Introduction to LangGraph], [https://langchain-ai.github.io/langgraph/ docs]
: [https://hf.co/learn/agents-course/unit3/agentic-rag/introduction Use Case for Agentic RAG]
:: [https://huggingface.co/learn/agents-course/unit3/agentic-rag/invitees tools]
: bonus
:: [https://hf.co/learn/agents-course/bonus-unit1/introduction Fine-tuning an LLM for Function-calling]
:: [https://hf.co/learn/agents-course/bonus-unit2/introduction Agent Observability and Evaluation]

==== LLM Course ====
Introductory course about natural large language models (LLMs) and language processing (NLP) using libraries from the Hugging Face ecosystem &amp;ndash; Transformers, Datasets, Tokenizers, and Accelerate.

: [https://hf.co/course/chapter0/1 '''LLM Course''']
:: [https://hf.co/course/chapter1/1 Transformer models]
::: [https://hf.co/course/chapter1/2 NLP and LLM], [https://hf.co/course/chapter1/3 What], [https://hf.co/course/chapter1/4 How], [https://hf.co/course/chapter1/5 Encoder], [https://hf.co/course/chapter1/6 Decoder], [https://hf.co/course/chapter1/7 Sequence-to-sequence], [https://hf.co/course/chapter1/8 Bias and limitations], 
:: [https://hf.co/course/chapter2/1 Using transformers]:
::: [https://hf.co/course/chapter2/2 pipeline], [https://hf.co/course/chapter2/3 models], [https://hf.co/course/chapter2/4 tokenizer], [https://hf.co/course/chapter2/5 batching], decoding, padding, attention mask
:: [https://hf.co/course/chapter3/1 Fine-tuning a pretrained model]:
::: [https://hf.co/course/chapter3/2 Preprocessing]&lt;small&gt;: tokenization, padding&lt;/small&gt;, [https://hf.co/course/chapter3/3 Fine-tuning], [https://hf.co/course/chapter3/4 Full training], map, [https://hf.co/docs/datasets/index dataset], dynamic padding, batch, collate function, train, predict, evaluate, [https://github.com/huggingface/accelerate accelerate]
:: [https://hf.co/course/chapter4/1 Sharing models and tokenizers]:
::: [https://hf.co/course/chapter4/2 Using], [https://hf.co/course/chapter4/3 Sharing]: push_to_hub, upload_file, Repository, git lfs, [https://hf.co/course/chapter4/4 Model card]
:: [https://hf.co/course/chapter5/1 The datasets library]:
::: [https://hf.co/course/chapter5/2 Loading dataset], [https://hf.co/course/chapter5/3 Slicing], batch, DataFrame, validation, splitting, [https://hf.co/course/chapter5/4 Big]: streaming, [https://hf.co/course/chapter5/5 Creating], [https://hf.co/course/chapter5/6 Semantic search]: embedding, [https://faiss.ai/ FAISS]
:: [https://hf.co/course/chapter6/1 The tokenizers library]:
::: [https://hf.co/course/chapter6/2 Training tokenizer], [https://hf.co/course/chapter6/3 Fast], grouping, [https://hf.co/course/chapter6/3b QnA], [https://hf.co/course/chapter6/4 Pre-tokenization], ([https://hf.co/docs/tokenizers/api/models models],[https://hf.co/docs/tokenizers/api/trainers trainers]), [https://hf.co/course/en/chapter6/5 Byte-Pair Encoding (BPE)], [https://hf.co/course/chapter6/6 WordPiece], [https://hf.co/course/chapter6/7 Unigram], [https://hf.co/course/chapter6/8 Building]: [https://hf.co/docs/tokenizers/api/post-processors post processors], [https://hf.co/docs/tokenizers/components#decoders decoders]
:: [https://hf.co/course/chapter7/1 Main nlp tasks]:
::: [https://hf.co/course/chapter7/2 Token classification], metrics, perplexity, [https://hf.co/course/chapter7/3 Fine-tuning a masked LM], [https://hf.co/course/chapter7/4 Translation], [https://hf.co/course/chapter7/5 Summarization], [https://hf.co/course/chapter7/6 CLM], [https://hf.co/course/chapter7/7 QnA]
:: [https://hf.co/course/chapter8/1 How to ask for help]
::: [https://hf.co/course/chapter8/2 Error], [https://hf.co/course/chapter8/3 Forums], [https://hf.co/course/chapter8/4 Debugging], [https://hf.co/course/chapter8/5 Issue]
:: [https://hf.co/course/chapter9/1 Gradio Demos]
::: [https://hf.co/course/chapter9/2 Building], [https://hf.co/course/chapter9/3 Interface class], [https://hf.co/course/chapter9/4 Sharing], [https://hf.co/course/chapter9/5 Integration], [https://hf.co/course/chapter9/7 Gradio Blocks]
:: [https://hf.co/course/chapter10/1 Curate high-quality datasets]
:: [https://hf.co/course/chapter11/1 Fine-tune Large Language Models]
:: [https://hf.co/course/chapter12/1 Build Reasoning Models]
:: [https://hf.co/course/events/1 Course Events]

==== Hugging Face docs ====
: https://hf.co/docs
: [https://hf.co/spaces/HuggingFaceTB/smol-training-playbook The Smol Training Playbook: The Secrets to Building World-Class LLMs]
===== Core libraries =====
::: [https://hf.co/docs/transformers Transformers] &amp;ndash; State-of-the-art ML for Pytorch, TensorFlow, and JAX.
:::: [https://hf.co/docs/transformers/pipeline_tutorial Inference, Tutorials]
::::: {{colbegin|2}} Run inference with pipelines, Write portable code with AutoClass, Preprocess data, Fine-tune a pretrained model, Train with a script, Set up distributed training with Accelerate, Load and train adapters with PEFT, Share your model, Agents 101, Agents, supercharged - Multi-agents, External tools, and more, Generation with LLMs, Chatting with Transformers {{colend}}
::::: [https://hf.co/docs/transformers/pipeline_tutorial Pipline]
::::: [https://hf.co/docs/transformers/llm_tutorial LLM]
::::: [https://hf.co/docs/transformers/conversations Chat]
:::: Tasks
::::: [https://hf.co/docs/transformers/tasks/sequence_classification NLP]
:::::: Text classification, Token classification, Question answering, Causal language modeling, Masked language modeling, Translation, Summarization, Multiple choice
::::: [https://hf.co/docs/transformers/tasks/audio_classification Audio], [https://hf.co/docs/transformers/tasks/image_classification Vision],[https://hf.co/docs/transformers/tasks/image_captioning Multimodal], [https://hf.co/docs/transformers/generation_strategies Generation], [https://hf.co/docs/transformers/tasks/idefics Prompting]
:::: [https://hf.co/docs/transformers/fast_tokenizers Developer guides]
:::: [https://hf.co/docs/transformers/quantization/overview Quantization]
:::: [https://hf.co/docs/transformers/performance Performance]
:::: [https://hf.co/docs/transformers/contributing Contributing]
:::: [https://hf.co/docs/transformers/philosophy Conceptual guides]
:::: [https://hf.co/docs/transformers/main_classes/agent API]
::::: [https://hf.co/docs/transformers/main_classes/pipelines#transformers.pipeline pipeline] &amp;ndash; simple interface for inference with models.
::::: ...
:::: [https://hf.co/docs/transformers/model_doc/albert Text models]
:::: [https://hf.co/docs/transformers/internal/modeling_utils Internal helpers]
:::: [https://hf.co/docs/transformers/model_doc/auto#auto-classes Auto classes]: AutoConfig, AutoModel, and AutoTokenizer. The from_pretrained method.
:::: [https://hf.co/docs/transformers/main_classes/trainer#transformers.Trainer Trainer] and [https://hf.co/docs/transformers/main_classes/trainer#transformers.TrainingArguments TrainingArguments] 
:::: [https://hf.co/docs/transformers/main/en/glossary Glossary]
::::: [https://huggingface.co/docs/transformers/main/en/glossary#head model head]
::: [https://hf.co/docs/datasets Datasets] &amp;ndash; Access and share datasets for computer vision, audio, and NLP tasks.
:::: [https://hf.co/docs/datasets/tutorial Tutorials]
:::: [https://hf.co/docs/datasets/how_to How-to guides]
:::: [https://hf.co/docs/datasets/about_arrow Conceptual guides]
:::: [https://hf.co/docs/datasets/package_reference/main_classes Reference]
::: [https://hf.co/docs/accelerate Accelerate] &amp;ndash; Easily train and use PyTorch models with multi-GPU, TPU, mixed-precision.
::: [https://hf.co/docs/tokenizers Tokenizers] &amp;ndash; Fast tokenizers, optimized for both research and production.
:::: Main components: Normalizers, Pre-tokenizers, Models, Post-Processors, Decoders
:::: More APIs: ... Input Sequences, Encode Inputs, Tokenizer, Encoding, Added Tokens, Visualizer

===== More docs =====
:: [https://hf.co/docs/hub Hub] &amp;ndash; Host Git-based models, datasets and Spaces on the Hugging Face Hub.
:: [https://hf.co/docs/diffusers Diffusers] &amp;ndash; State-of-the-art diffusion models for image and audio generation in PyTorch.
:: [https://hf.co/docs/huggingface_hub Hub Python Library] &amp;ndash; Client library for the HF Hub: manage repositories from your Python runtime.
:: [https://hf.co/docs/huggingface.js Huggingface.js] &amp;ndash; A collection of JS libraries to interact with Hugging Face, with TS types included.
:: [https://hf.co/docs/transformers.js Transformers.js] &amp;ndash; Community library to run pretrained models from Transformers in your browser.
:: [https://hf.co/docs/api-inference Inference API (serverless)] &amp;ndash; Experiment with over 200k models easily using the serverless tier of Inference Endpoints.
:: [https://hf.co/docs/inference-endpoints Inference Endpoints (dedicated)] &amp;ndash; Easily deploy models to production on dedicated, fully managed infrastructure.
:: [https://hf.co/docs/peft PEFT] &amp;ndash; Parameter efficient fine-tuning methods for large models
::: [https://hf.co/docs/peft/tutorial/peft_model_config Tutorial]
::: [https://hf.co/docs/peft/task_guides/prompt_based_methods PEFT method guides]
:::: LoRA, IA3
::: [https://hf.co/docs/peft/developer_guides/model_merging Developer guides]
:::: Model merging, Quantization, LoRA, Custom models, Adapter injection, Mixed adapter types, torch.compile, Contribute to PEFT, Troubleshooting, PEFT checkpoint format
::: [https://hf.co/docs/peft/accelerate/deepspeed Acceselerate]
:::: DeepSpeed, Fully Sharded Data Parallel
::: [https://hf.co/docs/peft/conceptual_guides/adapter Conceptual guides]
:::: Adapters, Soft prompts: Prompt tuning, Prefix tuning, P-tuning, Multitask prompt tuning, CPT; IA3, OFT/BOFT
::: [https://hf.co/docs/peft/package_reference/auto_class API reference]
:::: [https://hf.co/docs/peft/package_reference/auto_class Main classes]
::::: AutoPeftModel, PEFT model, PEFT types, Configuration, Tuner
:::: [https://hf.co/docs/peft/package_reference/adalora Adapters]
::::: {{colbegin|2}} AdaLoRA, IA3, Llama-Adapter, LoHa, LoKr, LoRA, X-LoRA, LyCORIS, Multitask Prompt Tuning, OFT, BOFT, Polytropon, P-tuning, Prefix tuning, Prompt tuning, Layernorm tuning,   VeRA, FourierFT, VB-LoRA, HRA, CPT, Bone{{colend}}
::: [https://hf.co/docs/peft/package_reference/merge_utils Utilities]
:::: Model merge, Helpers, Hotswapping adapters
:: [https://hf.co/docs/optimum Optimum] &amp;ndash; Fast training and inference of HF Transformers with easy to use hardware optimization tools.
:: [https://hf.co/docs/optimum-neuron AWS Trainium &amp;amp; Inferentia] &amp;ndash; Train and Deploy Transformers &amp;amp; Diffusers with AWS Trainium and AWS Inferentia via Optimum
:: [https://hf.co/docs/evaluate Evaluate] &amp;ndash; Evaluate and report model performance easier and more standardized.
::: types: metrics, comparisons, measurements
:: [https://hf.co/tasks Tasks]
::: extraction, question answering, classification, generation ...
:: [https://hf.co/docs/dataset-viewer Dataset viewer] &amp;ndash; API to access the contents, metadata and basic statistics of all Hugging Face Hub datasets.
::: Splits and subsets, [https://github.com/huggingface/dataset-viewer dataset-viewer]
:: [https://hf.co/docs/trl TRL] &amp;ndash; Transformer Reinforcement Learning
:::  reward modeling, fine-tuning, optimizations, 
:: [https://hf.co/docs/sagemaker Amazon SageMaker] &amp;ndash; Train and Deploy Transformer models with Amazon SageMaker and Hugging Face Deep Learning Containers (DLC).
:: [https://hf.co/docs/timm timm] &amp;ndash; Pytorch Image Models.
::: State-of-the-art computer vision models, layers, optimizers, training/evaluation, and utilities.
:: [https://hf.co/docs/safetensors Safetensors] &amp;ndash; Simple, safe way to store and distribute neural networks weights.
:: [https://hf.co/docs/text-generation-inference Text Generation Inference (TGI)] &amp;ndash; Toolkit to serve Large Language Models.
::: Conceptual Guides
::::  [https://hf.co/docs/text-generation-inference/conceptual/chunking V3 update, caching and chunking]
::::  [https://hf.co/docs/text-generation-inference/conceptual/streaming Streaming]
::::  [https://hf.co/docs/text-generation-inference/conceptual/quantization Quantization]
::::  [https://hf.co/docs/text-generation-inference/conceptual/tensor_parallelism Tensor Parallelism]
::::  [https://hf.co/docs/text-generation-inference/conceptual/paged_attention PagedAttention]
::::  [https://hf.co/docs/text-generation-inference/conceptual/safetensors Safetensors]
::::  [https://hf.co/docs/text-generation-inference/conceptual/flash_attention Flash Attention]
::::  [https://hf.co/docs/text-generation-inference/conceptual/speculation Speculation (Medusa, ngram)]
::::  [https://hf.co/docs/text-generation-inference/conceptual/guidance How Guidance Works (via outlines)]
::::  [https://hf.co/docs/text-generation-inference/conceptual/lora LoRA (Low-Rank Adaptation)]
::::  [https://hf.co/docs/text-generation-inference/conceptual/external External Resources]

:: [https://hf.co/docs/text-embeddings-inference Text Embeddings Inference] &amp;ndash; Toolkit to serve Text Embedding Models.
:: [https://hf.co/docs/competitions Competitions] &amp;ndash; Create your own competitions on Hugging Face.
:: [https://hf.co/docs/bitsandbytes Bitsandbytes] &amp;ndash; Toolkit to optimize and quantize models.
:: [https://hf.co/docs/optimum-tpu Google TPUs] &amp;ndash; Deploy models on [https://cloud.google.com/tpu/docs Google TPUs] via Optimum.
:: [https://hf.co/docs/chat-ui Chat UI] &amp;ndash; Open source chat frontend, powers the [https://hf.co/chat HuggingChat] app.
:: Extras
::: [https://hf.co/docs/hugs Hugging Face Generative AI Services (HUGS)] 
::: [https://hf.co/docs/leaderboards Leaderboards] &amp;ndash; Create your own Leaderboards on Hugging Face.
::: [https://hf.co/docs/autotrain AutoTrain] &amp;ndash; AutoTrain API and UI.
:::: [https://hf.co/autotrain autotrain]
::: [https://huggingface.co/docs/smolagents/index smolagents]

===Videos===
* [https://www.youtube.com/watch?v=5sLYAQS9sWQ How Large Language Models Work]
* [https://www.youtube.com/watch?v=JhCl-GeT4jw Large Language Models and The End of Programming - CS50 Tech Talk with Dr. Matt Welsh]
* [https://www.youtube.com/watch?v=yBI1nPep72Q LMStudio Tutorial Run ANY Open-Source Model LOCALLY]
* [https://www.youtube.com/watch?v=UU1WVnMk4E8 Create a Large Language Model from Scratch with Python – Tutorial]
* [https://www.youtube.com/watch?v=eC6Hd1hFvos Fine-tuning Large Language Models (LLMs) | w/ Example Code]

===Data sets===
* [https://hf.co/blog/Pclanglais/two-trillion-tokens-open Releasing the largest multilingual open pretraining dataset]
:: [https://hf.co/datasets/PleIAs/common_corpus Common Corpus]
:: [https://hf.co/datasets/PleIAs/common_corpus/tree/main Files and versions]

==See also==
* [[Computer science]]
* [[Artificial intelligence]]
* [[Machine learning]]
* [[Artificial Intelligence &amp; Machine Learning]]
* [[Artificial Intelligence and Robotics Laboratory]]
* [[Artificial Consciousness]]
* [[Supersymmetric Artificial Neural Network]]
* [[History of artificial intelligence]]

[[Category: Computer science]]
[[Category: Machine learning]]
[[Category: Artificial intelligence]]</text>
      <sha1>3llg2ypd02nc6k7tccmb9h33mg0vzxw</sha1>
    </revision>
    <revision>
      <id>2833670</id>
      <parentid>2833664</parentid>
      <timestamp>2026-09-18T01:45:21Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>moving to subpage</comment>
      <origin>2833670</origin>
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      <text bytes="6847" sha1="qby5qul5chbti8anjgyp1cm2e9y8dbi" xml:space="preserve">{{Short description|Machine learning models designed for natural language processing}}
[[File:LLM-logo.svg|thumb]]
Large language models (LLM's) are software programs that are also known as a form of &quot;artificial intelligence&quot; (AI); LLM's are specifically an aspect of generative AI. This wiki area is for learning, teaching, and research related to LLM's. 
{{RightTOC}}
[[Image:Multiple attention heads.png|right|280px|thumb|An illustration of multiple attention heads, each having its own criteria of relevance of other tokens for one of the tokens within the scope of a context window. (For the purpose of illustration, the context window consists of only one sentence.]]

==Sub-pages==
* [[Large language models/Context economy of agent runs]] — why the cost of a multi-step agent run is dominated by repeated input, how to measure a run without double counting, and a controlled experiment on session length.
* [[/Readings and learning media/]]

==Discourse and ideas==
Here is discourse and ideas related to large language models. Perhaps once significantly developed/refined, some of these can have their own sub-page or become a unique learning resource. 
===Learning wikis as training data===
Unless laws change, Creative Commons content appears to be valid training data for LLM's. As LLM's progress and advance, more and more data can be utilized to training increasingly complex models. Learning wikis devoted to learning, teaching, and resource, that allow for original research and original content creation (related to learning, teaching, and research), can potentially be extremely valuable (in terms of educational value) for large language models. Perhaps in the future (if this does not already exist), large language models will be able to continuously be trained on, retain, and learn from new data and information. Perhaps in the future, an open source large language model could only be trained on Creative Commons data, and therefore, all generated content would also be licensed under Creative Commons. 

==Discussion questions==
Here are some learning and teaching oriented discussion questions related to large language models. Humans can use language and mental effort to explore these ideas collaboratively, or some of these could be used as prompts to see how an LLM might respond. 
* Would a large language model that is only trained on Creative Commons licensed data only be capable of generating responses to prompts that can also be rightly and correctly licensed under a Creative Commons license? 
* How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)? 
* What are some ethical considerations related to large language models that should be considered? 
* What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think? 
* How can large language models help to advance and accelerate technological automation in ways that will benefit all of humanity? 
* In what ways can large language models help programmers to code?
* Can music be thought of a language within the realm of large language models? 
* What is differentiable computing and how does differentiable computing relate to large language models? 
* How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? 

== Educational prompt ideas==
These are original prompt ideas regarding ways to learn about large language models, and also to explore using LLM's for learning, teaching, and research. Input these into your preferred LLM (without quotes) to see what results are generated. LLM's might produce interesting or useful answers in response to these prompts. Some of these prompts may be interesting or useful for discussions among and between humans. 

* &quot;Describe to me how large language models can be utilized for learning, teaching, and research. Do this in an about 200 word two paragraph mini essay. Explain it to me like I am a freshman in community college.&quot; 
* &quot;Give me a list of 12 ways that large language models can be utilized for learning, teaching, and research.&quot;
* &quot;How can LLM's be utilized to accelerate the pace of research and scientific discovery?&quot;
* &quot;What are some ethical considerations related to large language models that should be considered?&quot;
* &quot;What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think?&quot;
* &quot;What are some project ideas to integrate large language models in with humanoid robots, and/or other sorts of robots? Please give me 15 project ideas that can be relatively simple or extremely complex.&quot;
* &quot;Please search the Internet if possible. In what ways have university professors and academic researchers been using large language models in the last year? Please respond in list form.&quot;
* &quot;In what ways can large language models help programmers to code? Please provide me 8 examples and respond in list form.&quot;
* &quot;Can music be thought of a language within the realm of large language models?&quot;
* &quot;What is differentiable computing and how does differentiable computing relate to large language models?&quot;
* &quot;How can one fine tune an open source large language model?&quot;
* &quot;What are some popular state of the art open source large language models. Please search the internet as helpful and respond to me in list form.&quot;
* &quot;Please give me a list of important terminology that I should be aware of when working with and training open source large language models. Please be comprehensive. Please respond in list form. And please search the internet as helpful.&quot;
* &quot;What sort of hardware should I utilize to run the most competent open source large language models that I want to utilize for learning, teaching, and research? Please search the internet as helpful.&quot;
* &quot;How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? Please respond in list form.&quot;
* &quot;How can researchers utilize large language models to create theories, hypothesis, and to formulate potential research studies? Please respond in short paragraphs, but in list form.&quot;

==See also==
* [[Computer science]]
* [[Artificial intelligence]]
* [[Machine learning]]
* [[Artificial Intelligence &amp; Machine Learning]]
* [[Artificial Intelligence and Robotics Laboratory]]
* [[Artificial Consciousness]]
* [[Supersymmetric Artificial Neural Network]]
* [[History of artificial intelligence]]

[[Category: Computer science]]
[[Category: Machine learning]]
[[Category: Artificial intelligence]]</text>
      <sha1>qby5qul5chbti8anjgyp1cm2e9y8dbi</sha1>
    </revision>
    <revision>
      <id>2833673</id>
      <parentid>2833670</parentid>
      <timestamp>2026-09-18T01:48:25Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>added section Local AI. limitless peace.</comment>
      <origin>2833673</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7243" sha1="qh298wd1fb5msk15248o4zhy46plid9" xml:space="preserve">{{Short description|Machine learning models designed for natural language processing}}
[[File:LLM-logo.svg|thumb]]
Large language models (LLM's) are software programs that are also known as a form of &quot;artificial intelligence&quot; (AI); LLM's are specifically an aspect of generative AI. This wiki area is for learning, teaching, and research related to LLM's. 
{{RightTOC}}
[[Image:Multiple attention heads.png|right|280px|thumb|An illustration of multiple attention heads, each having its own criteria of relevance of other tokens for one of the tokens within the scope of a context window. (For the purpose of illustration, the context window consists of only one sentence.]]

==Sub-pages==
* [[Large language models/Context economy of agent runs]] — why the cost of a multi-step agent run is dominated by repeated input, how to measure a run without double counting, and a controlled experiment on session length.
* [[/Readings and learning media/]]

==Discourse and ideas==
Here is discourse and ideas related to large language models. Perhaps once significantly developed/refined, some of these can have their own sub-page or become a unique learning resource. 
===Learning wikis as training data===
Unless laws change, Creative Commons content appears to be valid training data for LLM's. As LLM's progress and advance, more and more data can be utilized to training increasingly complex models. Learning wikis devoted to learning, teaching, and resource, that allow for original research and original content creation (related to learning, teaching, and research), can potentially be extremely valuable (in terms of educational value) for large language models. Perhaps in the future (if this does not already exist), large language models will be able to continuously be trained on, retain, and learn from new data and information. Perhaps in the future, an open source large language model could only be trained on Creative Commons data, and therefore, all generated content would also be licensed under Creative Commons. 

==Discussion questions==
Here are some learning and teaching oriented discussion questions related to large language models. Humans can use language and mental effort to explore these ideas collaboratively, or some of these could be used as prompts to see how an LLM might respond. 
* Would a large language model that is only trained on Creative Commons licensed data only be capable of generating responses to prompts that can also be rightly and correctly licensed under a Creative Commons license? 
* How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)? 
* What are some ethical considerations related to large language models that should be considered? 
* What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think? 
* How can large language models help to advance and accelerate technological automation in ways that will benefit all of humanity? 
* In what ways can large language models help programmers to code?
* Can music be thought of a language within the realm of large language models? 
* What is differentiable computing and how does differentiable computing relate to large language models? 
* How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? 
* What are the pros and cons of local AI? 

== Educational prompt ideas==
These are original prompt ideas regarding ways to learn about large language models, and also to explore using LLM's for learning, teaching, and research. Input these into your preferred LLM (without quotes) to see what results are generated. LLM's might produce interesting or useful answers in response to these prompts. Some of these prompts may be interesting or useful for discussions among and between humans. 

* &quot;Describe to me how large language models can be utilized for learning, teaching, and research. Do this in an about 200 word two paragraph mini essay. Explain it to me like I am a freshman in community college.&quot; 
* &quot;Give me a list of 12 ways that large language models can be utilized for learning, teaching, and research.&quot;
* &quot;How can LLM's be utilized to accelerate the pace of research and scientific discovery?&quot;
* &quot;What are some ethical considerations related to large language models that should be considered?&quot;
* &quot;What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think?&quot;
* &quot;What are some project ideas to integrate large language models in with humanoid robots, and/or other sorts of robots? Please give me 15 project ideas that can be relatively simple or extremely complex.&quot;
* &quot;Please search the Internet if possible. In what ways have university professors and academic researchers been using large language models in the last year? Please respond in list form.&quot;
* &quot;In what ways can large language models help programmers to code? Please provide me 8 examples and respond in list form.&quot;
* &quot;Can music be thought of a language within the realm of large language models?&quot;
* &quot;What is differentiable computing and how does differentiable computing relate to large language models?&quot;
* &quot;How can one fine tune an open source large language model?&quot;
* &quot;What are some popular state of the art open source large language models. Please search the internet as helpful and respond to me in list form.&quot;
* &quot;Please give me a list of important terminology that I should be aware of when working with and training open source large language models. Please be comprehensive. Please respond in list form. And please search the internet as helpful.&quot;
* &quot;What sort of hardware should I utilize to run the most competent open source large language models that I want to utilize for learning, teaching, and research? Please search the internet as helpful.&quot;
* &quot;How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? Please respond in list form.&quot;
* &quot;How can researchers utilize large language models to create theories, hypothesis, and to formulate potential research studies? Please respond in short paragraphs, but in list form.&quot;

== Local AI ==
Local AI (AI on local hardware/on prem hardware) is becoming increasingly more common. 
* [https://x.com/PrismML/status/2100692248480596348?s=20 Ternary Bonsai 2 27B] - For example Ternary Bonsai 2 27B &quot;[...] is 9x smaller than its full-precision counterpart [Qwen3.8 27B] while retaining 98.2% of its aggregate benchmark performance.&quot;]

==See also==
* [[Computer science]]
* [[Artificial intelligence]]
* [[Machine learning]]
* [[Artificial Intelligence &amp; Machine Learning]]
* [[Artificial Intelligence and Robotics Laboratory]]
* [[Artificial Consciousness]]
* [[Supersymmetric Artificial Neural Network]]
* [[History of artificial intelligence]]

[[Category: Computer science]]
[[Category: Machine learning]]
[[Category: Artificial intelligence]]</text>
      <sha1>qh298wd1fb5msk15248o4zhy46plid9</sha1>
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  </page>
  <page>
    <title>African Arthropods/Crabroninae</title>
    <ns>0</ns>
    <id>316633</id>
    <revision>
      <id>2833750</id>
      <parentid>2833040</parentid>
      <timestamp>2026-09-18T10:41:42Z</timestamp>
      <contributor>
        <username>Alandmanson</username>
        <id>1669821</id>
      </contributor>
      <comment>/* Afrotropical Crabronidae */</comment>
      <origin>2833750</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5425" sha1="7fj2dhf8v13m6kq3vlj2574k54v4mmt" xml:space="preserve">= Afrotropical Crabronidae =

All [[w:Crabronidae|crabronid]] species known in the [[w:Afrotropical realm|Afrotropics]] are of the subfamily Crabroninae. Several species of the subfamily [[w:Dinetinae|Dinetinae]] are found in Egypt, Tunisia and Algeria ([[w:Palearctic realm|Palearctic]]).&lt;ref name=waspweb&gt;van Noort, S. 2024. WaspWeb: Hymenoptera of the World. https://www.waspweb.org/Apoidea/Crabronidae/Classification/index.htm (accessed on 5 February 2025)&lt;/ref&gt;

The tribes and genera were reviewed by Bohart and Menke (1976).&lt;ref name=BohartMenke1976&gt;Bohart, R.M. &amp; Menke, A. S. 1976. Sphecid Wasps of the World: a Generic Revision. University of California Press, Berkeley, California.&lt;/ref&gt;

== Tribe Crabronini ==
Genera include ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/378/mode/2up Encopognathus]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/380/mode/2up Entomognathus]'', ''[https://archive.org/details/bub%20gb%20FExMjuRhjpIC/page/418/mode/2up Arnoldita]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/396/mode/2up Crossocerus]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/418/mode/2up Dasyproctus]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/428/mode/2up Lestica]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/418/mode/2up Neodasyproctus]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/386/mode/2up Rhopalum]''
&lt;gallery mode=packed heights=200&gt;
Crabronina inaturalist 34356268.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Crossocerus|''Crossocerus'' sp.]])
Dasyproctus iN 27385880 a.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Dasyproctus|''Dasyproctus'' sp.]])
Lestica bibundica Jacobs 2025.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Dasyproctus|''Lestica bibundica'']])
&lt;/gallery&gt;

==Tribe Larrini==
Larrini have:
*Compound eyes that converge above (sometimes parallel in ''Parapiagetia'' and ''Gastrosericus'');
*Posterior ocelli reduced to scars.
For a detailed discussion of the tribe see [https://archive.org/details/bub_gb_FExMjuRhjpIC/page/225/mode/2up Bohart &amp; Menke (1976:226-286)]. Genera include ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/251/mode/2up Gastrosericus]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/281/mode/2up Holotachysphex]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/285/mode/2up Kohliella]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/257/mode/2up Larropsis]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/277/mode/2up Parapiagetia]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/281/mode/2up Prosopigastra]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/267/mode/2up Tachysphex]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/255/mode/2up Tachytella]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/259/mode/2up Tachytes]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/249/mode/2up Dicranorhina]'', ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/233/mode/2up Larra]'', and ''[https://archive.org/details/bub_gb_FExMjuRhjpIC/page/237/mode/2up Liris]''.&lt;br&gt;


See also: [[African Arthropods/South African wasp species of Subtribe Larrina|South African wasp species of Subtribe Larrina]]
&lt;gallery mode=packed heights=200&gt;
Dicranorhina kohli.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps (''[[w:Dicranorhina|Dicranorhina kohli]]'')
Liris haemorrhoidalis iN 47526569 04.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Liris (wasp)|''Liris haemorrhoidalis'']])
Liris on Crassula iN 42678436 01.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Liris (wasp)|''Liris haemorrhoidalis'']])
Tachysphex specie edit1.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Tachysphex |''Tachysphex'' sp.]])
Tachysphex iN 250449986 2024 10 09 7305.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Tachysphex |''Tachysphex'' cf ''asinus'']])
Tachytes iN 188902572 1964.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Tachytes |''Tachytes'' sp.]])
&lt;/gallery&gt;

== Tribe Miscophini==
&lt;gallery mode=packed heights=200&gt;
Miscophus kriechbaumeri 2026-03-05.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Miscophus |''Miscophus kriechbaumeri'']])
Paranysson iN 199673489 1.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Paranysson|''Paranysson'' sp.]])
&lt;/gallery&gt;

== Tribe Oxybelini ==
&lt;gallery mode=packed heights=200&gt;
Oxybelus iN 250449990 2024 10 09 - 02.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Oxybelus|''Oxybelus'' sp.]])
Oxybelus iN 250450006 2024-10-09 07.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Oxybelus|''Oxybelus'' sp.]])
&lt;/gallery&gt;

== Tribe Palarini ==
&lt;gallery mode=packed heights=200&gt;
Palarus inaturalist 11100580 01.jpg|A banded beepirate (''Palarus latifrons'', Crabronidae) with a bee
Palarus_inaturalist_11100580_02.jpg|A banded beepirate (''Palarus latifrons'', Crabronidae) at the entrance to a bee hive
Palarus_Bee_Pirate_iN_144133368_2022-12-01_01.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Palarus|''Palarus pentheri'']])
&lt;/gallery&gt;

== Tribe Trypoxylini ==
&lt;gallery mode=packed heights=200&gt;
Pison iN 144131685 2022-11-30 03.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Pison|''Pison transvaalense'']])
Trypoxylon iN 99063113 a.jpg|[[w:Crabronidae|Crabronidae]] - sand wasps ([[w:Trypoxylon|''Trypoxylon'' sp.]])
&lt;/gallery&gt;

==References==
{{reflist}}

{{BookCat}}</text>
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====Cross-domain AI topics====
=====Wikipedia readings=====
&lt;/includeonly&gt;
: {{w|Adversarial machine learning}}
: {{w|AI alignment}}
: {{w|Attention (machine learning)}}
: {{w|Backpropagation}}
: {{w|Deep learning}}
: {{w|Embedding (machine learning)}}
: {{w|Fairness (machine learning)}}
: {{w|Feature learning}}
: {{w|Fine-tuning (deep learning)}}, SFT &amp;ndash; supervised fine-tuning
: {{w|Loss function}}
: {{w|Mechanistic interpretability}}
: {{w|Multilayer perceptron}} (MLP)
: {{w|Overfitting|Overfitting and Underfitting}}
: {{w|Reinforcement learning}}, RLVR - or Reinforcement Learning with Verifiable Rewards
:: {{w| https://en.wikipedia.org/wiki/Policy_gradient_method#Group_Relative_Policy_Optimization_(GRPO)|GRPO - Group Relative Policy Optimization}}
: {{w|Reinforcement learning from human feedback}}
: {{w|Supervised learning}} / {{w|Unsupervised learning}}
: {{w|Training, validation, and test data sets}}
: {{w|Transfer learning}}

=== Categories and lists (on Wikipedia) ===
: {{wc|Artificial intelligence laboratories}}
: {{wc|Artificial intelligence companies}}
: {{w|Glossary of artificial intelligence}}

===== Related rearning prompt ideas====
* Provide 8 examples of &quot;cross-domain AI topics&quot;. Briefly describe what &quot;Cross-domain AI topics&quot; are. Answer concisely and in list form. Do not be terse however. Be clear and understandable. 

[[Category:Artificial intelligence]]</text>
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====Cross-domain AI topics====
=====Wikipedia readings=====
&lt;/includeonly&gt;
: {{w|Adversarial machine learning}}
: {{w|AI alignment}}
: {{w|Attention (machine learning)}}
: {{w|Backpropagation}}
: {{w|Deep learning}}
: {{w|Embedding (machine learning)}}
: {{w|Fairness (machine learning)}}
: {{w|Feature learning}}
: {{w|Fine-tuning (deep learning)}}, SFT &amp;ndash; supervised fine-tuning
: {{w|Loss function}}
: {{w|Mechanistic interpretability}}
: {{w|Multilayer perceptron}} (MLP)
: {{w|Overfitting|Overfitting and Underfitting}}
: {{w|Reinforcement learning}}, RLVR - or Reinforcement Learning with Verifiable Rewards
:: {{w| https://en.wikipedia.org/wiki/Policy_gradient_method#Group_Relative_Policy_Optimization_(GRPO)|GRPO - Group Relative Policy Optimization}}
: {{w|Reinforcement learning from human feedback}}
: {{w|Supervised learning}} / {{w|Unsupervised learning}}
: {{w|Training, validation, and test data sets}}
: {{w|Transfer learning}}

=== Categories and lists (on Wikipedia) ===
: {{wc|Artificial intelligence laboratories}}
: {{wc|Artificial intelligence companies}}
: {{w|Glossary of artificial intelligence}}

===== Related rearning prompt ideas=====
* Provide 8 examples of &quot;cross-domain AI topics&quot;. Briefly describe what &quot;Cross-domain AI topics&quot; are. Answer concisely and in list form. Do not be terse however. Be clear and understandable. 

[[Category:Artificial intelligence]]</text>
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      <text bytes="1479" sha1="663zn57vyglivqdc6e2q1c2zcwk9u1b" xml:space="preserve">This area is for learning about studying cross-domain AI topics.
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====Cross-domain AI topics====
=====Wikipedia readings=====
&lt;/includeonly&gt;
: {{w|Adversarial machine learning}}
: {{w|AI alignment}}
: {{w|Attention (machine learning)}}
: {{w|Backpropagation}}
: {{w|Deep learning}}
: {{w|Embedding (machine learning)}}
: {{w|Fairness (machine learning)}}
: {{w|Feature learning}}
: {{w|Fine-tuning (deep learning)}}, SFT &amp;ndash; supervised fine-tuning
: {{w|Loss function}}
: {{w|Mechanistic interpretability}}
: {{w|Multilayer perceptron}} (MLP)
: {{w|Overfitting|Overfitting and Underfitting}}
: {{w|Reinforcement learning}}, RLVR - or Reinforcement Learning with Verifiable Rewards
:: {{w| https://en.wikipedia.org/wiki/Policy_gradient_method#Group_Relative_Policy_Optimization_(GRPO)|GRPO - Group Relative Policy Optimization}}
: {{w|Reinforcement learning from human feedback}}
: {{w|Supervised learning}} / {{w|Unsupervised learning}}
: {{w|Training, validation, and test data sets}}
: {{w|Transfer learning}}

=== Categories and lists (on Wikipedia) ===
: {{wc|Artificial intelligence laboratories}}
: {{wc|Artificial intelligence companies}}
: {{w|Glossary of artificial intelligence}}

===== Related learning prompt ideas=====
* Provide 8 examples of &quot;cross-domain AI topics&quot;. Briefly describe what &quot;Cross-domain AI topics&quot; are. Answer concisely and in list form. Do not be terse however. Be clear and understandable. 

[[Category:Artificial intelligence]]</text>
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====Cross-domain AI topics====
=====Wikipedia readings=====
&lt;/includeonly&gt;
: {{w|Adversarial machine learning}}
: {{w|AI alignment}}
: {{w|Attention (machine learning)}}
: {{w|Backpropagation}}
: {{w|Deep learning}}
: {{w|Embedding (machine learning)}}
: {{w|Fairness (machine learning)}}
: {{w|Feature learning}}
: {{w|Fine-tuning (deep learning)}}, SFT &amp;ndash; supervised fine-tuning
: {{w|Loss function}}
: {{w|Mechanistic interpretability}}
: {{w|Multilayer perceptron}} (MLP)
: {{w|Overfitting|Overfitting and Underfitting}}
: {{w|Reinforcement learning}}, RLVR - or Reinforcement Learning with Verifiable Rewards
:: {{w| https://en.wikipedia.org/wiki/Policy_gradient_method#Group_Relative_Policy_Optimization_(GRPO)|GRPO - Group Relative Policy Optimization}}
: {{w|Reinforcement learning from human feedback}}
: {{w|Supervised learning}} / {{w|Unsupervised learning}}
: {{w|Training, validation, and test data sets}}
: {{w|Transfer learning}}

=== Categories and lists (on Wikipedia) ===
: {{wc|Artificial intelligence laboratories}}
: {{wc|Artificial intelligence companies}}
: {{w|Glossary of artificial intelligence}}

===== Related learning prompt ideas =====
* Provide 8 examples of &quot;cross-domain AI topics&quot;. Briefly describe what &quot;Cross-domain AI topics&quot; are. Answer concisely and in list form. Do not be terse however. Be clear and understandable. 

[[Category:Artificial intelligence]]</text>
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=====Wikipedia readings=====
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: {{w|Adversarial machine learning}}
: {{w|AI alignment}}
: {{w|Attention (machine learning)}}
: {{w|Backpropagation}}
: {{w|Deep learning}}
: {{w|Embedding (machine learning)}}
: {{w|Fairness (machine learning)}}
: {{w|Feature learning}}
: {{w|Fine-tuning (deep learning)}}, SFT &amp;ndash; supervised fine-tuning
: {{w|Loss function}}
: {{w|Mechanistic interpretability}}
: {{w|Multilayer perceptron}} (MLP)
: {{w|Overfitting|Overfitting and Underfitting}}
: {{w|Reinforcement learning}}, RLVR - or Reinforcement Learning with Verifiable Rewards
:: {{w| https://en.wikipedia.org/wiki/Policy_gradient_method#Group_Relative_Policy_Optimization_(GRPO)|GRPO - Group Relative Policy Optimization}}
: {{w|Reinforcement learning from human feedback}}
: {{w|Supervised learning}} / {{w|Unsupervised learning}}
: {{w|Training, validation, and test data sets}}
: {{w|Transfer learning}}

=== Categories and lists (on Wikipedia) ===
: {{wc|Artificial intelligence laboratories}}
: {{wc|Artificial intelligence companies}}
: {{w|Glossary of artificial intelligence}}

==== Related learning prompt ideas ====
* Provide 8 examples of &quot;cross-domain AI topics&quot;. Briefly describe what &quot;Cross-domain AI topics&quot; are. Answer concisely and in list form. Do not be terse however. Be clear and understandable. 

[[Category:Artificial intelligence]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Qwertuy.png|thumb|right|thumb|150px|'''Figure 1'''. Couple in disagreement]]

; Scenario

Ethan and his partner, Mia, have a heated argument about household chores. Overwhelmed, Ethan goes for a long run (suppression – adaptive, giving him space to cool down). However, in the days that follow, he avoids the subject completely (denial/avoidance – blocking resolution).
{{RoundBoxBottom}}

Arguments, setbacks, and criticism are unavoidable in daily life. How individuals respond to these challenges often determines whether the experiences promote growth or perpetuate cycles of stress and conflict. What matters is not simply the stressful event itself, but the psychological strategies people use to defend against the painful emotions it evokes. 

Consider Ethan and his partner, Mia. After clashing over household chores, Ethan initially copes by going for a long run. This suppression is adaptive because it helps him regulate his anger and return to the conversation later with greater composure. Yet, when Ethan continues to avoid the subject in the following days, he slips into denial and avoidance, strategies that may reduce tension in the moment but leave the deeper conflict unresolved. Over time, this pattern begins to erode communication and intimacy within the relationship. 

Ethan’s experience illustrates the central theme of this chapter: defence mechanisms are double-edged psychological strategies. They are automatic, often unconscious responses that aim to shield the individual from anxiety, guilt, or emotional overload (Cramer, 1998). Originating in psychoanalytic theory and later refined through emotion regulation research, defence mechanisms reveal how people navigate the complex balance between protecting the self and engaging with reality (Gross, 1998). At their best, they provide temporary relief and allow time to regroup. At their worst, they distort perception, prevent resolution of difficulties, and contribute to long-term distress. 

Adaptive defences such as humour, reappraisal, or suppression can preserve relationships and promote wellbeing by reducing emotional intensity without undermining problem-solving. For instance, reappraising negative feedback as constructive can encourage resilience in academic or workplace settings. In contrast, maladaptive or avoidant defences such as denial, projection, and disengagement may soothe emotions in the short term but typically block constructive coping, leading to worsening anxiety, relational strain, or impaired performance (Vaillant, 2000; Bonanno &amp; Burton, 2013). 

These dynamics raise several important questions that guide this chapter. By exploring these questions, this chapter highlights how understanding defence mechanisms is not only essential for psychological science but also for practical applications in relationships, education, workplaces, and mental health.

{{RoundBoxTop|theme=3}}
'''Focus questions'''
[[File:Focus Questions.png|100px|thumb|right|'''Figure 2'''. Questions]]

*How can the same defence mechanism switch between adaptive and avoidant?
*What psychological processes influence whether a defence helps or harms?
*What are the long-term outcomes of relying on avoidance?
*How can people shift from avoidance to more constructive strategies?
{{RoundBoxBottom}}

== What are defence mechanisms? ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Psychoanalytic origins ===
The concept of defence mechanisms originates from the work of Sigmund Freud (1926), who proposed that the human psyche consists of three interacting structures: the id, ego, and superego. The id represents instinctual drives, the superego reflects moral and social standards, and the ego mediates between the two. According to Freud, when the ego is threatened by unacceptable impulses or overwhelming conflict, it deploys defence mechanisms as unconscious strategies to reduce anxiety and preserve psychological stability. 

Building on this foundation, Anna Freud (1936) systematically described and classified a range of defences that individuals rely upon in everyday life. Among the most widely recognised are: 
* Denial, in which an individual refuses to acknowledge distressing realities, such as ignoring the symptoms of illness. 
* Projection, where one attributes their own unacceptable feelings or impulses to another person (for example, accusing someone else of hostility when one is experiencing anger). 
* Regression, a reversion to earlier developmental behaviours, such as a stressed adult engaging in childlike outbursts. 
* Displacement, in which negative emotions are redirected toward a safer or less threatening target, such as venting workplace frustrations at home. 

From this psychoanalytic perspective, defences were considered largely unconscious and necessary for psychological survival. However, Freud and his successors also recognised that excessive or rigid reliance on these mechanisms could distort reality, block self-awareness, and interfere with personal growth. 

=== Contemporary perspectives ===
Modern psychology has reinterpreted defence mechanisms, integrating them into broader frameworks of coping and emotion regulation. Gross (1998) argued that many defences can be understood as automatic regulation strategies that shape emotional responses either before or after emotions are fully activated. For example, suppression resembles a response-focused strategy, while reappraisal aligns with antecedent-focused regulation. 

Contemporary research suggests that defences: 
* Exist on a continuum from mature to immature, with mature strategies (e.g., humour, suppression) linked to resilience, and immature strategies (e.g., denial, projection) associated with distress and dysfunction (Vaillant, 2000). 
* Are functionally equivalent to many processes studied in emotion regulation, indicating that psychoanalysis and cognitive psychology may be describing overlapping phenomena in different terms. 
* Are predictive of wellbeing: reliance on mature strategies fosters healthier relationships and better coping, whereas chronic use of maladaptive defences predicts anxiety, depression, and impaired functioning (Cramer, 1998; 2000). 

This modern perspective highlights that defence mechanisms are not inherently pathological; rather, their adaptiveness depends on flexibility, frequency, and context. In some situations, they provide necessary short-term relief, while in others, they may hinder long-term adjustment and growth.

{| class=&quot;wikitable&quot;
|+Table 1. Psychoanalytic vs. Contemporary perspectives on defence mechanisms
!Aspect
!Psychoanalytic (Freud, A. Freud)
!Contemporary (Gross, Vaillant, Cramer)
|-
|Nature
|Unconscious, rigid
|Automatic but flexible
|-
|Purpose
|Protect ego from anxiety
|Regulate emotion, maintain function
|-
|Adaptiveness
|Often pathological
|Continuum from adaptive to maladaptive
|-
|Link to wellbeing
|Secondary consideration
|Strong predictor of resilience vs. distress
|}

== Adaptive vs. maladaptive defences ==
Defence mechanisms are not inherently good or bad; their impact depends largely on the timing, context, and flexibility with which they are used. In some situations, a defence can provide valuable psychological protection and allow time to recover, while in others the same defence may lead to avoidance, strained relationships, or ongoing distress. Understanding this distinction is crucial for identifying when defences help and when they hinder.

[[File:Adaptivevsavoidant.png|150px|thumb|center|'''Figure 3'''. Adaptive vs Avoidant Defences]]'''Adaptive defences''' 

Adaptive defences reduce distress while still allowing individuals to remain connected to reality and, importantly, to take constructive action. These strategies are generally associated with resilience, psychological health, and effective emotional regulation (Vaillant, 2000). They are sometimes referred to as “mature” defences because they help manage stress without creating new problems. 
* '''Suppression''' involves consciously choosing to delay emotional expression until the time and place feels appropriate. For example, a teacher might feel frustrated with a disruptive class but suppresses the irritation until after the lesson, ensuring professional composure. By postponing rather than denying feelings, suppression protects both the individual and their social relationships. 
* '''Humour''' allows people to reframe difficulties in a lighter way that reduces tension. For instance, a medical professional might use a small joke to ease a patient’s anxiety before a procedure. Humour helps preserve emotional balance while maintaining social bonds. 
* '''Reappraisal''' is the process of altering how a situation is interpreted before emotions escalate (Gross, 1998). A student who receives critical feedback may view it as a personal attack or, through reappraisal, as an opportunity to improve. The latter interpretation reduces distress and supports motivation. 

These examples highlight how adaptive defences protect wellbeing while keeping individuals engaged with reality and with others. 

'''Maladaptive defences''' 

By contrast, maladaptive defences distort reality or prevent engagement with problems. They often provide immediate relief from anxiety but at the expense of long-term health, functioning, and relationships.{{f}}

* '''Denial''' involves refusing to acknowledge painful realities, such as ignoring medical symptoms or dismissing financial difficulties. While denial may temporarily reduce anxiety, it often delays necessary action and worsens outcomes. 
* '''Projection''' attributes one’s own unacceptable feelings to others. For example, a person who feels hostility may accuse a colleague of being aggressive. This defence deflects responsibility but can damage trust and communication. 
* '''Disengagement''' is characterised by withdrawal from responsibilities or relationships. A university student who avoids lectures after poor grades may feel immediate relief from performance anxiety, but long-term academic success is compromised. 

'''The continuum principle''' 

A crucial point is that defences operate on a continuum. The same mechanism can shift from adaptive to maladaptive depending on rigidity and duration (Cramer, 1998). For instance, suppression may be adaptive if it provides time to process emotions, but maladaptive if used habitually to avoid intimacy. Similarly, humour can strengthen resilience when used appropriately, but when employed to deflect vulnerability it may block deeper connections. This insight aligns with research on regulatory flexibility, which suggests that wellbeing depends less on which strategy is used and more on the capacity to shift flexibly between them (Bonanno &amp; Burton, 2013).

{| class=&quot;wikitable&quot;
|+Table 2. Adaptive vs. avoidant defence mechanisms
!Defence
!Adaptive use
!Avoidant use
|-
|Suppression
|Temporarily postponing anger during a meeting
|Habitually bottling emotions, leading to stress
|-
|Humour
|Lightening tension in a difficult conversation
|Using sarcasm to deflect vulnerability
|-
|Denial
|Briefly ignoring stress to focus on immediate tasks
|Refusing to acknowledge illness or relationship issues
|-
|Projection
|Redirecting energy into creative expression (sublimation)
|Blaming others for one’s own hostility
|}

{{RoundBoxTop|theme=1}}
'''Learning refreshers'''

When does suppression become avoidant?

a) When used once in a crisis

'''b) When prolonged and rigid ✅'''

c) When paired with humour
{{RoundBoxBottom}}

== Defence mechanisms and emotion regulation ==
Psychologist James Gross (1998) suggested that many defence mechanisms can be understood as part of a bigger system called emotion regulation. Instead of treating defences as mysterious or separate from everyday life, his model shows how people naturally try to manage emotions before or after they arise.

[[File:Emotionregulation.png|150px|thumb|center|'''Figure 4'''. Gross's Model of Emotion Regulation]]

Vaillant’s hierarchy of defences{{g}}. George Vaillant (2000) organised defence mechanisms into a hierarchy, ranging from mature defences (such as humour, altruism, and suppression), which are linked with psychological health, to neurotic defences (like repression, displacement, or intellectualisation), which may provide temporary relief but create inner tension, and finally to immature defences (such as denial, projection, and passive aggression), which often distort reality and predict long-term maladjustment. Maya’s shift from reappraisal to projection and disengagement shows how moving down this hierarchy can undermine wellbeing.

Gross’s process model of emotion regulation{{g}}. Gross (1998) reframed defences within the language of emotion regulation. Antecedent-focused strategies, such as reappraisal, occur early in the emotion process and are usually adaptive. Response-focused strategies, such as suppression, occur later and often only mask distress without solving it. In their landmark study, Gross and John (2003) found that people who habitually used suppression reported lower social support and higher stress, whereas those who used reappraisal experienced better wellbeing and closer relationships. Maya’s case illustrates this progression clearly: her initial reappraisal fostered growth, but her later projection and disengagement functioned as avoidance, leaving her worse off.

Integration{{g}}. Both frameworks highlight the same principle: flexibility matters more than any single strategy. Adaptive strategies such as humour or reappraisal support growth when used appropriately, but rigid reliance on avoidance or denial predicts long-term problems (Bonanno &amp; Burton, 2013; Cramer, 1998).

=== Case study: Maya’s academic journey ===
{{RoundBoxTop|theme=3}}
'''Scenario'''
[[File:Maya'sAcademicJourney.png|100px|thumb|right|'''Figure 5'''. Maya's academic journey]]

Maya, a university student, receives disappointing feedback. She initially reframes the feedback as an opportunity to improve (reappraisal – adaptive), but later insists the lecturer is biased and avoids study altogether (projection and avoidance – maladaptive).
{{RoundBoxBottom}}

Maya, a second-year university student, submits an essay she had worked on for weeks. When the feedback comes back, it is more critical than she expected. Initially, Maya feels a pang of disappointment, but instead of letting that feeling overwhelm her, she reminds herself that feedback can be a tool for growth. By choosing to interpret the comments as constructive, she engages in cognitive reappraisal, an adaptive strategy that allows her to stay motivated and plan for improvement. At this stage, Maya’s approach is consistent with what psychologists call an antecedent-focused strategy changing her perspective before her emotions spiral (Gross, 1998). This response not only protects her confidence but also encourages learning, showing how adaptive defences can support long-term growth.

However, as the semester becomes busier and pressure mounts, Maya’s mindset begins to shift. She rereads the comments and starts telling herself that the lecturer is unfair or even biased. This marks a move into projection, one of Vaillant’s (2000) immature defences, where a person attributes their own uncomfortable feelings to others. By externalising her frustration, Maya temporarily reduces her discomfort but, in doing so, undermines her relationship with her lecturer and creates unnecessary tension. Research shows that projection and other immature defences often predict poorer relational outcomes and long-term distress (Berry et al., 2012).

Over the following weeks, Maya’s strategies continue to deteriorate. Rather than addressing the issues raised, she begins to avoid studying altogether. She skips tutorials, puts off reading, and avoids beginning her next essay. This pattern of disengagement is another form of maladaptive avoidance. While it brings momentary relief from performance anxiety, it also compounds her stress by leaving deadlines unmet. Meta-analytic work has confirmed that avoidance and suppression are strongly linked to higher levels of depression and anxiety (Aldao, Nolen-Hoeksema, &amp; Schweizer, 2010).

Maya’s journey demonstrates the continuum principle: the same stressful event can trigger both adaptive and maladaptive defences depending on how flexibly they are used. At first, her reappraisal was beneficial, but her later reliance on projection and avoidance shows how rigid, avoidant strategies can backfire. This insight is supported by research showing that flexibility in emotion regulation predicts resilience (Bonanno &amp; Burton, 2013), while experiential avoidance predicts maladjustment across many disorders (Hayes et al., 1996).

{{RoundBoxTop|theme=2}}

'''Reflection prompt''': Think about your own response to criticism. Do you tend to reframe feedback constructively, or avoid it through denial, projection, or disengagement?
{{RoundBoxBottom}}

=== Research evidence ===
'''Meta-analyses'''

* Aldao, Nolen-Hoeksema, &amp; Schweizer (2010) showed that maladaptive strategies like rumination, avoidance, and suppression are strongly linked with depression and anxiety.
* Hayes et al. (1996) demonstrated that experiential avoidance predicts psychopathology across a wide range of disorders.
* Berry et al. (2012) found that attachment styles shape relational strategies, influencing whether defences become adaptive or maladaptive.

'''Empirical studies.'''

* Gross &amp; John (2003) confirmed that chronic suppression correlates with lower wellbeing and strained relationships.
* Moore et al. (2014) showed that reappraisal interventions can reduce depressive symptoms, highlighting its practical value.
* Bonanno &amp; Burton (2013) found that flexibility in regulation predicted resilience following bereavement.
* Cramer (1998) distinguished between coping and defence, showing that rigid use of defences is linked with poorer adjustment.
* Garakani et al. (2014) highlighted how defence-related processes are considered even in legal and clinical decision-making, such as determining psychiatric capacity.

{| class=&quot;wikitable&quot;
|+Table 3. Selected empirical findings on defence mechanisms and outcomes
!Study
!Finding
|-
|Gross &amp; John (2003)
|Suppression predicted stress and poorer social support
|-
|Aldao et al. (2010)
|Avoidant strategies linked to psychopathology
|-
|Bonanno &amp; Burton (2013)
|Flexibility predicted resilience in bereaved individuals
|-
|Berry et al. (2012)
|Attachment influenced defensive patterns in relationships
|-
|Garakani et al. (2014)
|Defence-related reasoning relevant to psychiatric consent capacity
|}

{{RoundBoxTop|theme=3}}
'''Scenario'''
[[File:20250929 0253 Dual Perspectives at Work simple compose 01k68ksh1jfpernv8401b7ejw9.png|100px|thumb|Raj’s workplace stress]]

Raj, a mid-level manager, learns his department may face redundancies. At first, he uses humour to lighten tension and maintain morale, an adaptive strategy consistent with mature defences (Vaillant, 2000). Over time, however, anxiety grows, and he withdraws from meetings, slipping into disengagement and denial (Cramer, 1998). This provides short-term relief but damages his reputation and reduces his influence. Research shows such avoidant styles are linked with higher stress and weaker social support (Gross &amp; John, 2003), while also eroding trust in relationships (Berry et al., 2012).

Raj’s experience highlights the continuum principle: a defence that begins as adaptive can become maladaptive when rigidly applied. Ultimately, it is flexibility and context that determine whether a defence supports resilience or undermines wellbeing (Bonanno &amp; Burton, 2013).

'''Reflection prompt: Think of a time when you avoided a stressful work, study, or relationship situation. Did the avoidance protect you temporarily but create problems later, like Raj?'''{{RoundBoxBottom}}

=== Progressive case studies ===
# '''Ethan &amp; Mia''': Suppression gave Ethan time to calm down, but denial prolonged conflict and damaged intimacy.
# '''Maya''': Reappraisal fostered growth initially, but projection and avoidance led to disengagement.
# '''Raj (workplace stress)''': Joked about redundancy (humour – adaptive) but later withdrew from meetings (avoidance – maladaptive), reducing performance.

'''Reflection prompt:''' Which case resonates most with your own coping style?

== Short-term relief vs. long-term costs ==
One of the most important lessons about defence mechanisms is that what helps in the short run may become harmful if it becomes a long-term pattern. In moments of stress or emotional overload, avoidance-based strategies can feel like a quick fix, offering a sense of calm or distance from pain. However, this immediate comfort often comes at the expense of deeper psychological health, relationships, and growth.

[[File:Bandaid on cracked wall.png|thumb|right|150px|'''Figure 6'''. Band-aids may offer quick relief, but do not fix underlying cracks much like avoidant defences]]

=== Short-term benefits ===
In the short term, avoidance can act as a psychological buffer. Denial may allow a person to protect their self-esteem by pushing aside a painful reality, at least temporarily. For example, someone receiving worrying health news might initially dismiss its seriousness, giving themselves space to process the shock gradually. Similarly, suppression holding back strong emotions in the moment can sometimes prevent escalation of conflict. Picture a heated family argument where one person consciously decides not to lash out, reducing the chance of lasting damage. These brief benefits illustrate why defences are not inherently bad; they can serve an important protective role when used flexibly and sparingly.

=== Long-term costs ===
When avoidance becomes rigid and repetitive, however, the costs begin to outweigh the benefits. Research shows that chronic suppression places strain on the body, being linked to elevated stress levels and even conditions like hypertension (Gross &amp; John, 2003). At a relational level, denial and projection erode intimacy and trust, making it difficult for people to feel safe and understood by others (Berry et al., 2012). On a personal level, habitual avoidance can stall growth. By disengaging from challenges, individuals miss out on opportunities to learn resilience, develop coping skills, and strengthen their sense of self (Cramer, 1998).

== Trigger responses and behavioural outcomes ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Shifting from avoidance to adaptation ===
When life feels stressful, our minds often reach for quick ways to cope. These “in the moment” responses can be surprisingly effective, at least at first. But whether they help us grow or hold us back depends on what we do next.

=== Trigger responses and behavioural outcomes ===
Stressful situations often spark rapid defensive reactions. At times, these are useful, offering space to pause and regroup. Briefly stepping away from an argument, making a light joke, or using intellectualisation thinking about a problem in abstract terms can act as adaptive triggers, providing breathing room without distorting reality.

Yet when such strategies harden into habits, they risk slipping into avoidance. Denial, projection, and disengagement are common here. Instead of facing the issue, the person pushes it away. Hayes et al. (1996) call this experiential avoidance the attempt to escape uncomfortable feelings rather than address them. While soothing at first, it usually creates greater strain over time.

The key is that defences are part of a dynamic process, not fixed as “good” or “bad.” A strategy that begins protectively can harm if overused. For instance, suppression may prevent conflict in the moment but, when habitual, creates emotional distance and weakens intimacy.{{RoundBoxTop|theme=2}}'''Key points about triggers and outcomes'''
*Adaptive triggers: short withdrawal, humour, intellectualisation.
*Avoidant triggers: prolonged denial, projection, disengagement (Hayes et al., 1996).
*Dynamic process: a strategy can begin adaptively but turn avoidant when repeated rigidly.{{RoundBoxBottom}}
[[File:20250929 0148 Response Strategies Infographic simple compose 01k68g2wjbe8cr3a2ex1qcnkgp.png|thumb|100px|Trigger Responses]]

This perspective highlights a key insight across both defence theory and emotion regulation research: flexibility matters more than the strategy itself. People are not trapped by their first reaction. What makes the difference is recognising when a short-term defence is buying time and when it has become a wall that blocks growth.

==Learning features==
'''Case study:'''&lt;blockquote&gt;''Ethan and Mia’s conflict escalates.'' Ethan avoids conversations for a week, convincing himself the problem will “work itself out.” Mia feels unheard, leading to further strain.&lt;/blockquote&gt;

{{RoundBoxTop|theme=1}}
'''Guiding Questions'''

1. Which defences did Ethan use?

2. When were they adaptive and when avoidant?

3. How might reappraisal or problem-solving have shifted the outcome?

{{RoundBoxBottom}}

'''Check your understanding'''
[[File:QUIZ.png|80px]]
&lt;quiz display=&quot;simple&quot;&gt;
{Which of Ethan’s responses was adaptive?
|type=&quot;()&quot;}
- Projection
+ Suppression
- Denial

{Which factor determines whether a defence adapts or avoids?
|type=&quot;()&quot;}
- Personality alone
+ Context and flexibility
- Number of conflicts

{Which is an antecedent-focused strategy?
|type=&quot;()&quot;}
- Rumination
+ Reappraisal
- Suppression
&lt;/quiz&gt;

==Conclusion==
[[File:EmotionalBalanceIllustration.png|150px|thumb|center|'''Figure 8'''. Emotional Balance Illustration]]

Defence mechanisms are everyday psychological shields that help people manage distress and protect their sense of self. Their usefulness depends less on the type of defence and more on how flexibly it is applied. When they provide short-term space to regulate feelings and create room for re-engagement, they can be adaptive. But when they become rigid patterns of avoidance, they often trap individuals in cycles of stress, disconnection, and missed opportunities.

Research highlights this divide. Flexible strategies such as reappraisal and problem-solving are consistently linked with resilience and stronger relationships, as they regulate emotions without distorting reality. By contrast, chronic avoidance through denial, projection, or disengagement predicts higher stress, more conflict, and poorer wellbeing (Aldao, Nolen-Hoeksema, &amp; Schweizer, 2010; Hayes et al., 1996). The central insight is that adaptiveness depends on timing, context, and the ability to shift. A once-helpful defence can become harmful if overused, making awareness and flexibility the key to healthier coping.

{{tip|'''Key take-home messages:'''

*The same defence can be adaptive or avoidant depending on timing and context.
*Avoidant styles may ease tension initially but create long-term costs.
*Awareness of defence use can help individuals shift toward adaptive strategies, improving emotional health and relationships.}}

{{RoundBoxTop|theme=5}}'''Reflection activity: Spot your defence'''

Think back to your last stressful moment. What was your first reaction did you crack a joke, stay silent, get defensive, or step away?
Identify the strategy. Was it reappraisal, humour, suppression, denial, projection, or disengagement?

Ask yourself:
*Did this strategy help me move forward, or did it block me from re-engaging?
*If it was avoidant, what adaptive alternative (e.g., problem-solving, mindfulness, humour used constructively) might have worked better?
*Write down one defence you’d like to use more flexibly. What small change could you try the next time stress shows up?

'''Takeaway: Awareness is the first step. By naming your defence, you create the chance to choose differently next time.'''{{RoundBoxBottom}}

==See also==
* https://en.wikipedia.org/wiki/Defence_mechanism
* https://en.wikipedia.org/wiki/Emotional_self-regulation
* https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2025/Maladaptive_defence_mechanisms_and_distress

==References==
{{Hanging indent|1= 

Aldao, A., Nolen-Hoeksema, S., &amp; Schweizer, S. (2010). Emotion-regulation strategies across psychopathology: A meta-analytic review. ''Clinical Psychology Review, 30''(2), 217–237.

Berry, K., Wearden, A., Barrowclough, C., Oakland, L., &amp; Bradley, J. (2012). An investigation of adult attachment and the nature of relationships with voices. British Journal of Clinical Psychology, 51(3), 280–291. https://doi.org/10.1111/j.2044-8260.2011.02028.x

Bonanno, G. A., &amp; Burton, C. L. (2013). Regulatory flexibility: An individual differences perspective on coping and emotion regulation. Perspectives on Psychological Science, 8(6), 591–612. https://doi.org/10.1177/1745691613504116

Cramer, P. (1998). Coping and defense mechanisms: What's the difference? Journal of Personality, 66(6), 919–946. https://doi.org/10.1111/1467-6494.00037

Cramer, P. (2000). Defense mechanisms in psychology today: Further processes for adaptation. American Psychologist, 55(6), 637–646. https://doi.org/10.1037/0003-066X.55.6.637

Garakani, A., Shalenberg, E., Burstin, S. C., Brendel, R. W., &amp; Appel, J. M. (2014). Voluntary psychiatric hospitalization and patient-driven requests for discharge: A statutory review and analysis of implications for the capacity to consent to voluntary hospitalization. Harvard Review of Psychiatry, 22(4), 241–249. https://doi.org/10.1097/HRP.0000000000000042

Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/10.1037/1089-2680.2.3.271

Gross, J. J., &amp; John, O. P. (2003). Individual differences in two emotion regulation processes: Implications for affect, relationships, and well-being. Journal of Personality and Social Psychology, 85(2), 348–362. https://doi.org/10.1037/0022-3514.85.2.348

Hayes, S. C., Wilson, K. G., Gifford, E. V., Follette, V. M., &amp; Strosahl, K. D. (1996). Experiential avoidance and behavioral disorders: A functional dimensional approach to diagnosis and treatment. Journal of Consulting and Clinical Psychology, 64(6), 1152–1168. https://doi.org/10.1037/0022-006X.64.6.1152

OpenAI. (2025). Sora [AI image and video generation model]. OpenAI. https://openai.com/sora

Vaillant, G. E. (2000). Adaptive mental mechanisms: Their role in a positive psychology. American Psychologist, 55(1), 89–98. https://doi.org/10.1037/0003-066X.55.1.89

}}

==External links==
* https://dictionary.apa.org/defense-mechanism (APA)
*https://www.simplypsychology.org/defense-mechanisms.html (SimplePsychology)

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      <text bytes="38922" sha1="cebaw28d1fnr2zl9ono8elq212y0jk4" xml:space="preserve">{{title|Procastination and temporal discounting:&lt;br&gt;How does valuing immediate rewards over future outcomes contribute to procrastination?}}

==Overview==
{{RoundBoxTop|theme=7}}
[[File:Figure no.1.jpg|180px|thumb|right|'''Figure 1.''' Cartoon girl lounging, watching Netflix, procrastinating on her assignments.]]

;Scenario

Imagine Sara, a university student, staring at a blank Word document. She has two weeks to finish an essay. At first, she promises herself she’ll start early. But as the days pass, she finds herself binge-watching Netflix, scrolling social media, and telling herself: “I’ll start tomorrow.” Tomorrow becomes next week. The deadline looms, and suddenly she’s awake at 3 AM, frantically typing, exhausted and anxious.

{{RoundBoxBottom}}

Sara’s story is not unusual. Many people, whether students, professionals, or everyday decision-makers, struggle with putting off important tasks despite knowing the consequences{{f}}. This everyday behaviour {{g}} '''procrastination''' can be frustrating, even self-destructive. But why do we procrastinate, especially when the costs are so obvious?

One psychological explanation lies in the concept of temporal discounting the tendency to devalue rewards the further they are in the future. Immediate rewards like watching a show or checking social media feel more appealing than the distant reward of finishing an essay and getting a good grade. Temporal discounting provides a powerful lens for understanding procrastination because it shows how short-term emotions and impulses often outweigh long-term goals.

This chapter explores the link between procrastination and temporal discounting{{explain}}, reviewing theory, research, and strategies to overcome present bias. By examining both theoretical models and empirical evidence, this chapter will show how understanding temporal discounting offers powerful insights into procrastination and how strategies can be developed to overcome it.

{{RoundBoxTop|theme=6}}
'''Focus questions'''
*What is the relationship between temporal discounting and procrastination?
*Which psychological theories explain these behaviours?{{vague}}
*What does research reveal about effective interventions{{ic|for what?}}?
*How can individuals apply these {{which}} insights to improve self-control and wellbeing?
{{RoundBoxBottom}}

== Theoretical Foundations of Procrastination and Temporal Discounting ==
[[File:Figure02.jpg|150px|thumb|right|'''Figure 2.''' Factors contributing to procrastination include cognitive, emotional, and situational influences.]]

'''Understanding procrastination'''

Procrastination is commonly defined as the voluntary delay of an intended action despite expecting negative consequences (Steel, 2007){{ic|Not in References}}. Unlike ordinary delay, procrastination involves an irrational element: people knowingly undermine their own long-term goals. This makes procrastination both a self-regulation failure and a motivational paradox. For students like Sara, putting off an assignment rarely results from laziness; rather, it reflects a systematic preference for short-term relief from stress or boredom over long-term achievement.

'''The concept of temporal discounting''' 

[[File:Figure.03..jpg|180px|thumb|center|'''Figure 3.''' Illustration of temporal discounting: the subjective value of a reward decreases as the delay to its receipt increases]]

Temporal discounting, also referred to as delay discounting, describes the tendency to devalue rewards as the delay to their receipt increases (Ainslie, 1975; Mazur, 1987){{ic|Not in References}}. For example, many individuals would prefer $50 today over $100 in a year{{f}}. The concept originated in behavioural economics but has been widely applied in psychology to explain impulsive choices, addictions, and health behaviours{{f}}. Temporal discounting illustrates how the subjective value of outcomes shrinks with time, which directly contributes to procrastination—immediate comfort (watching Netflix) feels more valuable than a distant reward (a good grade).

'''Competing models of discounting''' 

Two mathematical models have been proposed to explain discounting: exponential and hyperbolic. Exponential models (Samuelson, 1937) assume a consistent rate of discounting across time. In contrast, hyperbolic models (Ainslie, 1975) predict that people disproportionately prefer immediate rewards over delayed ones, leading to inconsistent choices. Hyperbolic discounting explains Sara’s experience: a week before the deadline, finishing her essay seems worthwhile, but when the moment arrives, the temptation of instant entertainment overrides her plans. This inconsistency makes hyperbolic discounting particularly relevant to procrastination.

'''Temporal Motivation Theory(TMT)'''

Steel’s (2007) Temporal Motivation Theory (TMT) integrates procrastination research with discounting models. TMT proposes that motivation is determined by four variables:
*Expectancy (likelihood of success)
*Value (reward of the outcome)
*Impulsiveness (sensitivity to delay)
*Delay (time until reward)

These combine into the formula:

&lt;math&gt;Motivation = \frac{Expectancy * Value}{Impulsiveness * Delay}&lt;/math&gt;

According to TMT, procrastination occurs when expectancy and value are low (e.g., boring tasks with uncertain outcomes), and impulsiveness and delay are high (e.g., long deadlines). This framework links procrastination directly with temporal discounting by showing how delayed rewards lose motivational power.

'''Metacognitive prespectives on procrastination'''

Metacognition{{g}} the ability to reflect on one’s own thinking also plays a role in procrastination{{f}}. Individuals often recognise that delaying a task will create stress later, but awareness does not always translate into action. Research suggests that metacognitive beliefs (e.g., “I work better under pressure”) may maintain procrastination (Fernie &amp; Spada, 2008). From a theoretical perspective, this highlights the interaction between temporal discounting and self-regulation: people not only discount future rewards but also rationalise the decision, reinforcing the cycle.

'''Strengths and limitations of theoretical approaches '''

Each framework contributes uniquely to understanding procrastination. Hyperbolic discounting provides a precise model of time-inconsistent preferences but is limited in explaining why some individuals procrastinate more than others. TMT addresses this by incorporating personality factors such as impulsiveness and task aversiveness, offering a more comprehensive account. However, critics argue that TMT can be difficult to test empirically due to the complexity of its variables (van Eerde, 2016). Metacognitive perspectives broaden the picture by showing how beliefs and awareness shape procrastination, though these theories sometimes lack quantitative precision. Together, these models suggest that procrastination is best explained by a multifactorial approach linking temporal discounting, motivation, and cognition.
== Empirical Evidence on Procrastination and Temporal Discounting==
Understanding procrastination requires examining the substantial body of empirical research{{f}} linking it to temporal discounting. Studies{{f}} from behavioural economics, psychology, and education have consistently demonstrated that the tendency to overvalue immediate rewards and undervalue long-term outcomes contributes to persistent task delay. This section reviews laboratory experiments, survey and longitudinal findings, meta-analyses, and case-based applications, situating Sara’s story within the broader research landscape.

'''Academic Procrastination'''

Procrastination is highly prevalent among students. Surveys reveal that between 70–95% of college students {{where}} report procrastinating at least occasionally, with nearly 50% identifying as chronic procrastinators (Pychyl, 2013; Steel, 2007). Academic procrastination has been linked to poorer performance, higher stress, and reduced life satisfaction.

These findings illustrate that Sara’s struggle is not unique but rather part of a widespread behavioural pattern across higher education. Like many students, she experiences the tension between long-term academic goals (e.g., completing her assignment on time) and the pull of immediate, pleasurable alternatives.

'''Laboratory Studies on temporal Discounting and Procrastination'''

Experimental paradigms provide controlled environments to investigate the link between procrastination and temporal discounting. One widely used approach involves delay discounting tasks, where participants choose between smaller immediate rewards and larger delayed rewards (Ainslie, 1975; Kirby &amp; Herrnstein, 1995). These studies consistently show that individuals who demonstrate higher temporal discounting strong preference for immediate rewards also report higher procrastination tendencies (Sirois, 2014).

For example, Steel and König (2006) conducted a laboratory study with university students completing a series of hypothetical academic tasks. Students with a higher preference for immediate leisure over delayed academic outcomes were significantly more likely to postpone starting assignments, even when aware of negative consequences. This mirrors Sara’s experience: although she initially intended to start her essay early, the immediate reward of Netflix and social media outweighed her future goal of timely completion, leading to last-minute panic.

Moreover, hyperbolic discounting models suggest that individuals disproportionately favour very immediate rewards, creating a “now versus later” conflict. O’Donoghue and Rabin (1999) demonstrated that students frequently revise plans daily {{g}} intending to start work “tomorrow” but succumb to immediate temptations each evening, a phenomenon often{{f}} referred to as dynamic inconsistency. This mechanism can explain why Sara repeatedly postponed her essay despite good intentions.

''' Survey and Longitudinal Research on student Procrastination'''

Beyond laboratory paradigms, surveys provide ecological insights into procrastination behaviours among larger samples. Steel (2007) conducted a meta analysis of 80 studies, estimating that approximately 80–95% of university students {{where}} procrastinate at least occasionally. Temporal discounting, operationalised via self reported impulsivity and reward sensitivity, consistently predicted higher procrastination scores.

Longitudinal studies further indicate that procrastination is not merely situational but stable across time, influenced by individual differences in reward valuation. Sirois et al. (2019) tracked students {{where}} over a semester and found that high discounting of future academic outcomes predicted chronic assignment delay, poorer academic performance, and increased stress levels. In Sara’s case, her repeated delay across days illustrates the cumulative impact of discounting future outcomes: each day she prioritises immediate gratification, and the cumulative delay culminates in a high-stress, last-minute effort.

Additionally, survey research highlights affective correlates of procrastination. Students often report using immediate rewards as a mood regulation strategy (Tice &amp; Baumeister, 1997). Sara’s choice to binge-watch Netflix and scroll social media can be seen as an emotion-focused coping mechanism, temporarily reducing negative affect while inadvertently amplifying stress as deadlines approach.

'''Meta-Analyses and Systematic Reviews'''

Meta-analytic evidence provides robust support for the link between temporal discounting and procrastination. Sirois et al. (2017) reviewed 50 studies and reported a moderate positive correlation (r ≈ 0.35) between impulsive decision-making (high temporal discounting) and procrastination behaviours. Findings were consistent across cultural contexts, academic levels, and measurement methods, indicating a generalizable pattern.

A notable finding from these reviews is the interaction between cognitive capacity and temporal discounting. Individuals with stronger executive functions (working memory, inhibitory control) tend to discount the future less steeply and procrastinate less (Gustavson et al., 2014). This aligns with the concept that procrastination is not purely motivational but also cognitive: failure to inhibit immediate impulses or maintain future-oriented goals contributes to task delay.

'''Cognitive and emotional Correlates and Procrastination'''

Procrastination is intricately linked with cognitive and emotional processes. Executive function deficits, such as poor planning or reduced inhibitory control, increase susceptibility to temporal discounting (Sirois &amp; Kitner, 2015). Emotional factors including anxiety, fear of failure, and boredom further exacerbate procrastination.

For instance, the avoidance hypothesis posits that individuals delay tasks to avoid anticipated negative emotions (Solomon &amp; Rothblum, 1984). Sara may experience subtle anxiety about producing a high-quality essay, prompting her to distract herself with immediate pleasures. This emotional avoidance reinforces the present-biased behaviour characteristic of temporal discounting.

Moreover, affective states influence discounting rates. Positive moods can reduce perceived task aversiveness and lower procrastination (Tice et al., 2001), whereas negative moods heighten preference for immediate mood-enhancing activities. Such findings highlight the interplay between cognition, emotion, and time perception in understanding procrastination.

'''Intervention Studies Targeting Present Bias and Procrastination'''

Intervention research provides practical insights into mitigating procrastination by addressing temporal discounting. Commitment devices, where individuals pre-commit to future behaviours, effectively reduce delay (Ariely &amp; Wertenbroch, 2002). For example, students who schedule fixed writing times with penalties for non-compliance show reduced last-minute cramming{{f}}.

Other interventions include goal setting strategies, chunking large tasks into smaller components, and implementing immediate rewards for progress (van Eerde, 2003). Sara could benefit from breaking her essay into manageable segments with short-term incentives, effectively aligning immediate actions with delayed academic outcomes.

Cognitive-behavioural approaches targeting maladaptive beliefs about time and self-regulation also show promise (Rozental et al., 2018). By restructuring expectations and enhancing future-oriented planning, such interventions reduce reliance on immediate gratification, thereby countering the effects of temporal discounting.

'''Critical Analysis of Research Evidence'''

While empirical evidence{{f}} robustly links temporal discounting to procrastination, several limitations exist. Many studies {{f}} rely on self-report measures, susceptible to social desirability and recall biases. Laboratory tasks {{f}} , though controlled, may lack ecological validity, failing to fully capture real-world procrastination dynamics such as Sara’s essay scenario.

Furthermore, most research focuses on student populations, limiting generalizability to other age groups or occupational contexts. Cultural factors also influence discounting preferences and procrastination patterns, suggesting the need for cross-cultural replication (Henrich et al., 2010).

Finally, causal relationships remain complex. While temporal discounting predicts procrastination, reciprocal influences exist: repeated procrastination may alter perception of future rewards, creating a feedback loop. Future research should explore longitudinal and intervention designs to clarify causal mechanisms and practical applications.

'''Link to Sara’s Scenario'''

Sara’s procrastination exemplifies the mechanisms revealed in research. Her initial intention to start early reflects goal-directed behaviour, but preference for immediate rewards (Netflix, social media) aligns with temporal discounting tendencies observed in both lab and field studies. Emotional regulation strategies such as mood repair through distractions exacerbate the delay. When the deadline approaches, panic-induced cognitive overload mirrors findings that procrastination compounds stress and impairs performance (Sirois et al., 2019). This case demonstrates the utility of integrating experimental, survey, and intervention research to understand and potentially remediate procrastination.


==Integrating Theory and Research – Understanding Procrastination Through Temporal Discounting==
While theoretical models of procrastination and temporal discounting provide a framework for understanding why individuals delay tasks, empirical evidence{{f}} offers concrete insights into how these processes manifest in real life. This section integrates theory and research, demonstrating how temporal discounting explains procrastinatory behavior and how interventions can be informed by these findings. By connecting theory and evidence, we can develop a more comprehensive understanding of procrastination and identify strategies to reduce its impact.

'''Linking Theoretical Models with Empirical Findings'''

'''Temporal Motivation Theory and Empirical Support'''

Temporal Motivation Theory (TMT) proposes that the likelihood of completing a task depends on the perceived value, expectancy, delay, and sensitivity to time (Steel &amp; König, 2006). Empirical studies consistently support this framework:
*Tasks with high immediate rewards are more likely to be completed than those with delayed benefits.
*The preference for smaller, sooner rewards over larger, later rewards reflects a present bias, a core principle in temporal discounting.

Example: In a study by Sirois et al. (2019), college students who demonstrated steeper discounting rates were significantly more likely to procrastinate on academic assignments, confirming TMT predictions.

'''Hyperbolic Discounting and Real-World Behavior'''

Hyperbolic discounting explains why people value immediate rewards disproportionately compared to future rewards (Ainslie, 1975). Empirical evidence demonstrates that:
*Individuals with high procrastination scores tend to heavily discount delayed outcomes.
*Short-term temptations, such as social media or leisure activities, consistently override long-term goals, reinforcing procrastination patterns.

Example: A longitudinal study by van Eerde (2003) found that employees with higher temporal discounting rates reported more frequent delays in completing work tasks, illustrating the predictive power of hyperbolic discounting for everyday procrastination.

'''Explaining the Gap Between Intention and Action'''

Research{{f}} highlights a significant gap between individuals’ intentions and their actual behavior, a phenomenon explained by the interaction between procrastination and temporal discounting:
*Individuals often intend to work on a task but succumb to the lure of immediate gratification.
*This intention-behavior gap is particularly pronounced for tasks with delayed benefits, such as studying, exercising, or completing reports.

Example: Sara’s case illustrates this gap: despite knowing the benefits of completing her assignments early, she repeatedly chose short-term leisure activities, consistent with her high present bias.

'''Integrating Strategies with Theory and Evidence'''

Integrating interventions with theoretical insights enhances their effectiveness. For instance:
*Goal-setting and chunking tasks reduce perceived delay, lowering the influence of temporal discounting (Schraw et al., 2007).
*Immediate self-rewards or commitment devices leverage the preference for short-term rewards to encourage task completion (Rabinovich et al., 2019).

Mindfulness and cognitive restructuring help individuals become aware of their present bias and make more future-oriented decisions.

By connecting theory and empirical research, it becomes clear that procrastination is not simply laziness but a systematic response to present bias and temporal discounting. Integrating these insights enables the design of targeted interventions, improving both understanding and practical solutions for individuals like Sara.

== Strategies and Interventions to Overcome Procrastination ==
While understanding the causes of procrastination is critical, practical strategies are essential to mitigate its impact. Interventions targeting temporal discounting, executive functioning, and emotional regulation have shown{{f}} promise in reducing procrastination. This section explores evidence-based techniques, cognitive-behavioural strategies, and technological tools, with a focus on how these strategies can be applied in real-life scenarios, such as Sara’s struggle with completing her essay.

'''Behavioural Strategies to Manage Procrastination'''

Behavioural strategies focus on modifying actions and environmental cues to encourage task engagement. These techniques aim to counteract the pull of immediate rewards by increasing the salience or accessibility of delayed outcomes.

'''Time Management and Task Structuring'''

Effective time management involves breaking large tasks into smaller, achievable components, each with clear deadlines. Research indicates that goal-setting and task chunking reduce cognitive overload and improve adherence to long-term goals (Locke &amp; Latham, 2002).

Example: Sara could divide her essay into three parts: literature review, methodology, and conclusion, assigning specific deadlines for each. Immediate rewards, such as short breaks after completing each section, can reinforce progress and align her actions with future academic goals.

'''Use of Commitment Devices'''

Commitment devices are strategies that pre-commit individuals to specific behaviours, reducing the influence of present bias (Ariely &amp; Wertenbroch, 2002). These can include setting self-imposed deadlines, using apps that lock distracting websites, or arranging accountability with peers.

Example: Sara might set a public deadline with a friend or use a productivity app that blocks social media during work periods. Knowing she will face social or technical consequences helps her prioritize the essay over immediate leisure.

'''Cognitive-Behavioural Strategies'''

Cognitive-behavioural strategies target maladaptive thought patterns and beliefs that contribute to procrastination, enhancing self-regulation and long-term goal orientation.

'''Cognitive Restructuring'''

Procrastinators often hold irrational beliefs, such as “I work better under pressure” or “This task is too hard to start now.” Cognitive restructuring involves identifying these thoughts and replacing them with realistic, actionable beliefs (Rozental et al., 2018).

Example: Sara could challenge the thought, “I need to feel motivated to start,” replacing it with, “I can begin small; motivation often follows action.” This shift reduces avoidance and strengthens task initiation.

'''Implementation Intentions'''

Implementation intentions are “if-then” plans that link specific cues to desired actions (Gollwitzer, 1999). Research shows these plans improve follow-through by automating goal-directed behaviour and reducing reliance on willpower.

Example: Sara could adopt the plan: “If it is 6 PM, then I will write for 25 minutes without checking my phone.” The structured cue-action link decreases reliance on self-control and counters immediate temptations.

'''Emotional Regulation Techniques'''

Procrastination often serves as a coping mechanism for negative emotions. Interventions that target emotional regulation can reduce the appeal of immediate mood repair behaviours.

'''Mindfulness and Stress Reduction'''

Mindfulness practices help individuals observe impulses without acting on them, reducing reactive behaviour and enhancing tolerance for discomfort (Sirois &amp; Tosti, 2012). Stress reduction techniques, such as deep breathing or guided meditation, can also buffer the anxiety that triggers procrastination.

Example: Before starting her essay, Sara could engage in a 5-minute mindfulness exercise to acknowledge her anxiety about the task. This may reduce the urge to seek distraction through Netflix or social media.

'''Reward Substitution and Positive Reinforcement'''

Providing immediate, tangible rewards for progress can counterbalance the lure of present-biased activities. Research demonstrates that small, frequent reinforcers encourage persistence in delayed tasks (Locke &amp; Latham, 2002).

Example: Sara might reward herself with a favorite snack or 10 minutes of leisure after completing a subsection of her essay, effectively bridging the gap between immediate and delayed outcomes.

'''Technological and Environmental Interventions'''

Modern tools and environmental modifications can help mitigate procrastination by reducing distractions and enhancing accountability.

'''Productivity Apps and Digital Tools'''

Apps such as Forest, Focus@Will, or website blockers reduce the accessibility of distractions and provide visual cues of progress. Studies show these tools support sustained attention and increase task completion rates (Kim et al., 2019).

Example: Sara could use a timer app that blocks social media during her writing sessions, ensuring uninterrupted focus.

'''Environmental Structuring'''

Changing the physical environment to minimise distractions and facilitate task engagement improves adherence to long-term goals. This may include dedicated workspaces, limiting access to phones, or arranging study schedules with peers.

Example: Sara might designate a quiet corner of her room solely for essay writing, keeping her phone in another room, thereby reducing temptation to engage in immediate leisure.

'''Integrated Intervention Approaches'''

Integrated interventions combine behavioural, cognitive, emotional, and technological strategies for maximal effect. Research supports multi-component programs that include goal-setting, implementation intentions, mindfulness, and reinforcement schedules (Rozental et al., 2018; van Eerde, 2003).

Example: An ideal intervention for Sara could include:
*Breaking the essay into smaller tasks with daily deadlines.

*Using an “if-then” plan for writing sessions.

*Employing mindfulness to manage anxiety.

*Leveraging productivity apps to block distractions.

*Applying immediate rewards for task completion.

By simultaneously addressing cognitive, emotional, and behavioural factors, integrated approaches increase the likelihood of sustained behaviour change and reduce procrastination tendencies.

'''Critical Evaluation of Intervention Research'''

While interventions show promise, limitations exist. Many studies rely on short-term laboratory or self-report measures, leaving long-term efficacy unclear. Cultural and individual differences influence which strategies are most effective, and interventions must be tailored to personal preferences and contexts. Additionally, excessive reliance on external tools may reduce intrinsic motivation over time, highlighting the need for balanced approaches that cultivate internal self-regulation.

'''Link to Sara’s Scenario'''

Applying these strategies, Sara can transform her approach to essay writing. By breaking the task into manageable steps, scheduling structured writing sessions, and using mindfulness and digital tools to manage immediate temptations, she can overcome present bias and reduce procrastination. The integration of behavioural, cognitive, emotional, and environmental strategies aligns with empirical evidence, offering practical solutions to a common student challenge.

{{RoundBoxTop|theme=5}}
==Focus Questions and Reflection Activities==
{{Roundboxbottom}}

{{RoundBoxTop|theme=5}}
Focus Questions
*How does temporal discounting contribute to procrastination in academic and personal contexts?
*What immediate rewards influence procrastination despite long-term consequences?
*Which strategies are most effective in countering present bias?
*How can Sara implement small interventions to reduce procrastination?
*How do individual differences, such as impulsivity or anxiety, affect the success of interventions?
*How can technology support or hinder self-regulation?

'''Reflection Activities'''

Activity 1: Self-Assessment of Procrastination Patterns
*Identify tasks you commonly delay and the immediate rewards associated.
*Rate tasks by difficulty and immediacy of reward.
*Reflect on temporal discounting influences.

Activity 2: Behavioural Experiment
*Choose a delayed task.
*Apply a strategy (e.g., task chunking, implementation intention).
*Track time, stress, and completion outcome.

Activity 3: Temporal Discounting Exercise
*List short-term and long-term rewards for completing tasks.
*Rank them and practice reframing long-term rewards to feel more immediate.

Activity 4: Reflective Journaling
*Journal instances of procrastination, emotions, and strategies tried.
*Analyse patterns and identify effective interventions.
{{Roundboxbottom}}

'''Connecting Reflection to Theory'''

Through these activities, readers:
*Observe the impact of temporal discounting on daily behaviour.
*Test cognitive, behavioural, and environmental strategies.
*Personalise interventions to reduce procrastination and enhance self-regulation.

==Conclusion and Future Directions==

Procrastination remains a pervasive challenge across academic, professional, and personal domains. This chapter has explored the role of temporal discounting as a key cognitive mechanism underlying procrastination, reviewed empirical research, and examined strategies for overcoming present bias. The integration of behavioural, cognitive, emotional, and technological interventions offers practical pathways to reduce procrastination and improve goal-directed behaviour.

'''Summary of Key Findings'''
*Temporal Discounting as a Core Mechanism
Temporal discounting explains why immediate rewards are often preferred over delayed outcomes, even when long-term consequences are more valuable. Sara’s tendency to delay her essay exemplifies this bias, highlighting how short-term distractions compete with long-term academic goals.
*Cognitive and Emotional Contributors
Procrastination is influenced not only by temporal discounting but also by maladaptive beliefs, low self-regulation, and negative emotions such as anxiety and fear of failure. Cognitive restructuring and mindfulness practices target these underlying factors, enhancing task initiation and persistence.
*Effective Interventions
Evidence-based strategies, including goal-setting, task chunking, implementation intentions, commitment devices, and reward substitution, can mitigate procrastination. Technological tools and environmental modifications further support task engagement by reducing distractions and promoting accountability.
*Integrated Approach
Multi-component interventions that address behavioural, cognitive, emotional, and environmental domains demonstrate the greatest efficacy. Applying these strategies to Sara’s context—structured deadlines, mindfulness, and digital accountability—illustrates practical implementation of theoretical insights.

'''Implications for Theory and Practice'''

Understanding procrastination through the lens of temporal discounting has several theoretical and practical implications:
*Theoretical: Emphasising the role of present bias bridges research in behavioural economics, cognitive psychology, and self-regulation, offering a comprehensive framework for understanding procrastination.
*Practical: Interventions should be personalised, considering individual differences in impulsivity, motivation, and emotional regulation. For students like Sara, combining small, manageable tasks with immediate reinforcement can significantly improve productivity.

{{ic|The rest is over the maximum word count}}

'''Limitations and Considerations'''

Despite the insights provided, several limitations exist:
*Short-Term Focus of Many Studies
Many interventions have been evaluated in laboratory or short-term settings, leaving questions about long-term adherence and sustainability.
*Individual Differences
Factors such as personality traits, cultural background, and environmental context influence the effectiveness of strategies. Not all interventions may work equally well for everyone.
*Technology Dependence
Overreliance on apps and digital tools may reduce intrinsic motivation if external scaffolds are removed. Balancing external aids with internal self-regulation skills is crucial.

'''Future Research Directions'''

Future research could explore:
*Longitudinal Studies: Examining long-term outcomes of integrated interventions on procrastination and academic performance.		
*Personalised Approaches: Tailoring interventions based on individual differences in temporal discounting, impulsivity, and emotional regulation.
*Cross-Cultural Research: Investigating how cultural norms influence procrastination patterns and response to interventions.
*Technology Integration: Developing adaptive digital tools that combine feedback, gamification, and behavioural reinforcement while fostering intrinsic motivation.

'''Final Thoughts and Link to Sara’s Scenario'''

Sara’s case highlights the real-world impact of procrastination and the utility of theory-informed interventions. By understanding temporal discounting and implementing evidence-based strategies, she can overcome present bias, improve her academic performance, and develop long-term self-regulation skills. The insights from this chapter provide both a conceptual framework and practical toolkit applicable to a wide range of procrastination contexts, reinforcing the importance of bridging research and practice.

{{robelbox|theme=5|quiz}}
* '''Quick Quiz'''&lt;quiz display=&quot;simple&quot;&gt;
{Which of the following best describes temporal discounting?}
- Preferring immediate rewards over larger, delayed rewards.
+ Always prioritising long-term goals over short-term pleasures.
&lt;/quiz&gt;
{{roundboxbottom}}

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{{Hanging indent|1=

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‌
}}

==External links==
* 🔗 https://www.youtube.com/watch?v=ZUbQaC3uTg0]
*🔗 https://www.nature.com/articles/s41598-024-65110-4

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==Motivation==
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# [[/Emotion regulation through exercise/]] - How do people use exercise to regulate their emotional states? {{ME-By|KB3250298}}
# [[/Empathy and jury decision-making/]] - How does empathy toward defendants and victims influence jurors' reasoning and verdict decisions? {{ME-By|U3254168}}
# [[/Empathy fatigue and emotional exhaustion/]] - How does sustained empathic engagement contribute to emotional exhaustion? {{ME-By|U3143751}}
# [[/Enjoyment and learning/]] - How does enjoyment influence learning? {{ME-By|Diaz Chas}}
# [[/Envy in the workplace/]] - What role does envy play in workplace behaviour? {{ME-By|Flickstar888}}
# [[/Excitement as an emotion/]] - What is the emotion of excitement and how does it influence behaviour and wellbeing? {{ME-By|U3292769}}
# [[/Fear extinction/]] - What psychological and neural processes underlie the extinction of fear responses? {{ME-By|ChillPsychGuy0607}}
# [[/Growth mindset and psychological wellbeing/]] - How does a growth mindset influence psychological wellbeing? {{ME-By|Avj.06}}
# [[/Immersive therapy for PTSD treatment/]] - How does it work and what are the effects? {{ME-By|StretchBeyond}}
# [[/Interpersonal psychotherapy and emotion/]] - How does interpersonal psychotherapy improve emotional wellbeing through changes in relationships? {{ME-By|U3280122}}
# [[/Introjection and guilt-based motivation/]] - What role do shame and guilt play in introjected forms of behavioural regulation? {{ME-By|U3330981}}
# [[/Irritability/]] - What is irritability, what causes it, what are its consequences, and how can it be managed? {{ME-By|U3275992}}
# [[/Love styles and relationships/]] - How do love styles influence relationship satisfaction and stability? {{ME-By|U3246588}}
# [[/Melatonin and seasonal mood/]] - What role does melatonin play in seasonal mood changes? {{ME-By|U3224236}}
# [[/Mental health first aid and helping behaviour/]] - What motivates people to recognise, approach, and support someone with a mental health problem? {{ME-By|Katelyn Rod}}
# [[/Mood and cognitive performance/]] - How do different mood states impact attention, memory, and problem solving? {{ME-By|U3283879}}
# [[/Moodiness/]] - What is moodiness, why does it occur, and how can it be managed? {{ME-By|U3239251}}
# [[/Moral disgust and jury decision-making/]] - How does moral disgust influence jurors' judgments of guilt, blame, and punishment? {{ME-By|Yellowvines}}
# [[/Neurobiology of love/]] - What neural systems and biochemical processes underlie love? {{ME-By|Honeybelle11}}
# [[/Outdoor play and children's emotional well-being/]] - How does outdoor play influence children's emotional well-being? {{ME-By|Mymunu}}
# [[/Phubbing and emotion/]] - What are the emotional causes and consequences of phubbing? {{ME-By|U3243961}}
# [[/Positive emotion dysregulation/]] - What is positive emotion dysregulation and how does it affect psychological functioning? {{ME-By|P U3270518}}
# [[/Psychedelic treatment of eating disorders/]] - How might psychedelic-assisted therapy influence psychological mechanisms involved in eating eating disorders? {{ME-By|Leilab23}}
# [[/Responsiveness and interpersonal trust/]] - How does responsiveness foster trust in relationships? {{ME-By|U3282586}}
# [[/Romantic entertainment and love beliefs/]] - How does romantic entertainment influence beliefs and expectations about love and romantic relationships? {{ME-By|U3247927}}
# [[/Romantic jealousy/]] - Why does romantic jealousy occur, what are its impacts, and how can it be managed?{{ME-By|U3279062}}
# [[/Romantic rejection and emotional response/]] - What emotional responses does romantic rejection evoke and how can they be regulated? {{ME-By|U3275873}}
# [[/Secondary trauma in healthcare workers/]] - What are the emotional consequences of secondary trauma in healthcare settings? {{ME-By|U3257744}}
# [[/Seasonal affective disorder/]] - What is SAD, why does it occur, and how can it be managed? {{ME-By|Greg Philips}}
# [[/Self-blame and emotion/]] - How does self-blame influence emotional responses to negative events? {{ME-By|U3281277}}
# [[/Self-disclosure and emotional intimacy/]] - How does self-disclosure foster emotional closeness in relationships? {{ME-By|U3283302}}
# [[/Self-stigma and emotion/]] - How does self-stigma impact emotional well-being? {{ME-By|Pinkk47}}
# [[/Social connection and emotion regulation/]] - How do social relationships help regulate people's emotions? {{ME-By|U3284040}}
# [[/Socioemotional selectivity theory and wellbeing in ageing/]] - How do social and emotional experiences affect wellbeing as people age? {{ME-By|U3253354}}
# [[/Technology-based pain management/]] - How can technology-based tools alter pain perception and pain management? {{ME-By|ChelsSchofield}}
# [[/Time perception in mood disorders/]] - How do anxiety and depression alter the subjective experience of time? {{ME-By|Safiaah}}
# [[/Trust rebuilding after trauma/]] - How can trauma survivors develop trust in similar situations again? {{ME-By|U3284437}}
# [[/Volunteer wellbeing/]] - How does volunteering affect volunteers' subjective wellbeing? {{ME-By|U3216851}}

==Motivation and emotion==
# [[/Boredom and interest/]] - How do boredom and interest shape emotional and motivational states? {{ME-By|U3239431}}
# [[/Falling in love/]] - What motivational and emotional processes underlie romantic attraction and falling in love? {{ME-By|Mort006}}
# [[/Life purpose and well-being/]] - How does a sense of purpose contribute to well-being and how can it be cultivated? {{ME-By|U3286962}}
# [[/Moral emotions and ethical behaviour/]] - How do moral emotions motivate ethical and prosocial action? {{ME-By|U3263365}}
# [[/Oxytocin as a neuromodulator/]] - What are the motivational and emotional effects of oxytocin as a neuromodulator? {{ME-By|U3306498}}
# [[/Reinforcement sensitivity theory/]] - How does reinforcement sensitivity theory explain individual differences in motivation and emotion? {{ME-By|UU3231448}}
# [[/Reward prediction error/]] - How does discrepancy between expected and actual rewards influence learning, emotion, and motivation? {{ME-By|Aivy.uc.cbr}}
# [[/Warm-glow giving/]] - Why does giving feel good and how does this influence prosocial behaviour? {{ME-By|Karabi Tasneem}}
# [[/Wisdom, motivation, and emotion/]] - How do motivational and emotional processes contribute to wisdom? {{ME-By|Med.011387}}

[[Category:Motivation and emotion/Book/2026]]</text>
      <sha1>9o618394llv3va0406qjxpeyexkqxhs</sha1>
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  </page>
  <page>
    <title>User talk:Pine</title>
    <ns>3</ns>
    <id>327857</id>
    <revision>
      <id>2833640</id>
      <parentid>2833045</parentid>
      <timestamp>2026-09-17T19:51:03Z</timestamp>
      <contributor>
        <username>~2026-40514-81</username>
        <id>3101893</id>
      </contributor>
      <comment>/* Hi Pine */ trying again</comment>
      <origin>2833640</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1173" sha1="t85zv57ogsoplp1o3y40e45dx7ih4de" xml:space="preserve">== How to contact me ==

Please contact me on my Meta talk page at [[:meta:User talk:Pine]]. --[[User:Pine|Pine]] ([[User talk:Pine|discuss]] • [[Special:Contributions/Pine|contribs]]) 07:29, 22 February 2026 (UTC)

== Hi Pine ==
Hi Pine,

A few months ago you posted an invitation on the colloquium about something that required participation on meta. I responded and explained that I am blocked on Meta and therefore cannot participate, even though I am still considered a wikimedia movement member (for example I am not blocked on Wikiversity). I also remember that you were quite friendly and offered help in response to my post

Would you be interested in passing on some recent problems I have come across?

[[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 14:22, 13 September 2026 (UTC)
:: Hi again {{PAGENAME}},
:: I know that you want users to contact you on the EngLish Wikipedia, just to let you know I am indef blocked there so cannot comply. I hope you don't mind me tring to reach you twice? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 19:50, 17 September 2026 (UTC)</text>
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  <page>
    <title>Athena problem</title>
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      <timestamp>2026-09-18T07:26:37Z</timestamp>
      <contributor>
        <username>Athene241</username>
        <id>3100061</id>
      </contributor>
      <origin>2833720</origin>
      <model>wikitext</model>
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      <text bytes="158875" sha1="kdwogyjdmav3l9d0mnl1b3b6xzkrll5" xml:space="preserve">{{mathematics}}
'''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' &gt; 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the &quot;[[:w:Prime number|prime number]] [[:w:Greater than|&gt;]] ''b''&quot; [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, &quot;string&quot; is a subsequence of &quot;meistersinger&quot;. In contrast, 758 is not a subsequence of 378259, &quot;abc&quot; is not a subsequence of &quot;cbacacba&quot;, since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]])

Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|&gt;]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''&lt;sub&gt;''b''&lt;/sub&gt; := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' &gt; 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''.

By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}.

Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers &gt; ''b'', whose set is exactly the Athena set in base ''b'').

Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''&lt;sub&gt;''b''&lt;/sub&gt;) (i.e. to compute the Athena set in base ''b''), where ''L''&lt;sub&gt;''b''&lt;/sub&gt; is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|&gt;]] ''b'', for 2 ≤ ''b'' ≤ 36.

For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes &gt; ''b'' or probable primes &gt; ''b'' with length ≤ 100000. (The chance that an unproven probable prime in these sets is in fact composite is less than 10&lt;sup&gt;−2000&lt;/sup&gt;, see https://t5k.org/notes/prp_prob.html)

Below, family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') means sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), where the members are expressed as base ''b'' strings, like the numbers in https://stdkmd.net/nrr/aaaab.htm, https://stdkmd.net/nrr/abbbb.htm, https://stdkmd.net/nrr/aaaba.htm, https://stdkmd.net/nrr/abaaa.htm, https://stdkmd.net/nrr/abbba.htm, https://stdkmd.net/nrr/abbbc.htm, e.g. 1{3} (in decimal) is the numbers in https://stdkmd.net/nrr/1/13333.htm#about_first, and {1}3 (in decimal) is the numbers in https://stdkmd.net/nrr/1/11113.htm#about_first, and 31{3} (in decimal) is the numbers in https://stdkmd.net/nrr/3/31333.htm#about_first, and {1}31 (in decimal) is the numbers in https://stdkmd.net/nrr/1/11131.htm#about_first, and 1{2}3 (in decimal) is the numbers in https://stdkmd.net/nrr/1/12223.htm#about_first, also, superscripts always means exponents, subscripts are always used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 = 123333567, all subscripts are written in decimal.

== Solve the problem ==

To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime &gt; ''b'' in all such families.

We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') &quot;linear&quot; families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows:

* 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''.
* 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by:
* 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''.
* 2.2. If possible, simplify the family.
* 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers &gt; ''b''), and if so then remove the family from ''L''.
* 3. Update ''L'', after each split examine the new families as in step 2.

e.g. in decimal (base ''b'' = 10):

''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991}

''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9}

and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1

and since the family 2{0}1 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1

221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L''

none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L''

and since the family 3{0,3,6,9}3 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

etc.

Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime &gt; ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime &gt; ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime &gt; ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both &quot;numbers of Athena primes in base ''b''&quot; and &quot;length of the largest Athena prime in base ''b''&quot; are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;.

Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'')

* If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and the string ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and both the strings ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' and ''xy''&lt;sub&gt;2&lt;/sub&gt;''y''&lt;sub&gt;1&lt;/sub&gt;''z'' represent a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}''z'' ∪ ''x''{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.

e.g. in decimal (base ''b'' = 10):

* 2221 is a prime &gt; 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
* 227 is a prime &gt; 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
* 449 is a prime &gt; 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
* Both 5051 and 5501 are primes &gt; 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
* 8501 is a prime &gt; 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
* 887 is a prime &gt; 10, and it is a subsequence of 2887, also 2087 is a prime &gt; 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
* 349 and 449 are primes &gt; 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes &gt; 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
* 251, 281, 521, 821, 881 are primes &gt; 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes &gt; 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''&lt;sub&gt;1&lt;/sub&gt;, ''y''&lt;sub&gt;2&lt;/sub&gt;, ..., ''y''&lt;sub&gt;''n''&lt;/sub&gt;}, then we can replace ''x''{''Y''}''z'' by ''xy''&lt;sub&gt;1&lt;/sub&gt;{''Y''}''z'' ∪ ''xy''&lt;sub&gt;2&lt;/sub&gt;{''Y''}''z'' ∪ ... ∪ ''xy''&lt;sub&gt;''n''&lt;/sub&gt;{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]].

If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base ''b'' = 10):

* The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
* The smallest prime in the family {5}1 is 555555555551.
* The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'').

The following is a &quot;[[:w:Semi-algorithm|semi-algorithm]]&quot; that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement:

# ''M'' = ''[[:w:Empty string|∅]]''
# while (''L'' ≠ ''∅'') do
# choose ''x'', a shortest string in ''L''
# ''M'' := ''M'' ∪ {''x''}
# ''L'' := ''L'' − ''sup''({''x''})

In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&amp;#39;, some regular overapproximation to ''L'', until we can show ''L''&amp;#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&amp;#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''&lt;sub&gt;1&lt;/sub&gt;{''L''&lt;sub&gt;2&lt;/sub&gt;}''L''&lt;sub&gt;3&lt;/sub&gt;, where each of ''L''&lt;sub&gt;1&lt;/sub&gt;, ''L''&lt;sub&gt;2&lt;/sub&gt;, ''L''&lt;sub&gt;3&lt;/sub&gt; is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not.

Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]).

To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime &gt; ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2&lt;sup&gt;''n''−2&lt;/sup&gt; strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length &gt; (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' &lt; ''b'', i.e. finding the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (or prove such prime does not exist) with ''k'' &lt; ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is &lt; ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist) (in fact, it is known that exactly what bases 2 ≤ ''b'' ≤ 1024 have the families listed in the table below as unsolved families, all of these families in all bases 2 ≤ ''b'' ≤ 1024 have been searched to length ≥ 10000 (for the family (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1), bases 2 ≤ ''b'' ≤ 1048576, searched to length ≥ 5000)): (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)):

'''Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' for some ''n'' ≥ 0?'''

An [[:w:Algorithm|algorithm]] to solve this problem, for example, would allow us to decide if there are any additional [[:w:Fermat prime|Fermat prime]]s other than the known ones (corresponding to ''n'' = 0, 1, 2, 3, 4). To see this, take ''b'' = 2, ''x'' = 1, ''y'' = 0, and ''z'' = 0&lt;sub&gt;16&lt;/sub&gt;1. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;+1 is prime then ''n'' must be a [[:w:Power of 2|power of two]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Fermat prime. Besides, it would allow us to decide if there are infinitely many [[:w:Mersenne prime|Mersenne prime]]s (of the form 2&lt;sup&gt;''p''&lt;/sup&gt;−1 with prime ''p''). To see this, take ''b'' = 2, ''x'' = ''𝜆'' (the [[:w:Empty string|empty string]]), ''y'' = 1, and ''z'' = 1&lt;sub&gt;''n''+1&lt;/sub&gt;, where ''n'' is the exponent of the Mersenne prime which we want to know whether it is the largest Mersenne prime or not. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;−1 is prime then ''n'' must be a [[:w:Prime number|prime]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Mersenne prime. Also, it would allow us to decide whether 78557 is the smallest [[:w:Sierpinski number|Sierpinski number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;''n''&lt;/sup&gt;+1 is composite for all ''n'' ≥ 1) and whether 509203 is the smallest [[:w:Riesel number|Riesel number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;*n*&lt;/sup&gt;−1 is composite for all ''n'' ≥ 1), etc.

'''Conjecture (this conjecture is very important for the Athena problem): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes).'''

(in fact, this conjecture is equivalent to the conjecture (to prove this, by change the base (''b'') to a power of ''b'' which is larger than the largest prime in a given family (in base ''b'') which only contains finitely many primes): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains at least one prime (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains at least one prime), like the [[:w:Bunyakovsky conjecture|Bunyakovsky conjecture]] and the [[:w:Dickson's conjecture|Dickson's conjecture]] and the [[:w:Schinzel's hypothesis H|Schinzel's hypothesis ''H'']], if such ''n'' always exists, then there must be always infinitely many such ''n'', to prove this, add another polynomial for the cases of the Dickson's conjecture and the Schinzel's hypothesis ''H'', also, change the polynomial (e.g. change ''n'' to ''r''×''n'' or ''n''&lt;sup&gt;''r''&lt;/sup&gt; for all integers ''r'' &gt; 1) for the cases of the Bunyakovsky conjecture and the Schinzel's hypothesis ''H'')

Some families can be ruled out to contain no prime &gt; ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''&lt;sup&gt;4&lt;/sup&gt;+4×''y''&lt;sup&gt;4&lt;/sup&gt;]]), or combine of them, e.g.

* The base 9 family 2{7}: Always divisible by 2 or 5
* The base 11 family 2{5}: Always divisible by 2 or 3
* The base 14 family B{0}1: Always divisible by 3 or 5
* The base 13 family 95{0}3: Always divisible by 5, 7, or 17
* The base 16 family {4}D: Always divisible by 3, 7, or 13
* The base 16 family {8}F: Always divisible by 3, 7, or 13
* The base 21 family {7}D: Always divisible by 2, 13, or 17
* The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79
* The base 9 family {1}: Can be written as (9&lt;sup&gt;''n''&lt;/sup&gt;−1)/8 and can be factored as (3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 8
* The base 8 family 1{0}1: Can be written as 8&lt;sup&gt;''n''&lt;/sup&gt;+1 and can be factored as (2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (4&lt;sup&gt;''n''&lt;/sup&gt;−2&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 9 family 3{8}: Can be written as 4×9&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 16 family 1{5}: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−1)/3 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 3
* The base 16 family {4}1: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−49)/15 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−7) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+7) / 15
* The base 27 family 7{Q}: Can be written as 8×27&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (4×9&lt;sup&gt;''n''&lt;/sup&gt;+2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 27 family 9{G}: Can be written as (125×27&lt;sup&gt;''n''&lt;/sup&gt;−8)/13 and can be factored as (5×3&lt;sup&gt;''n''&lt;/sup&gt;−2) × (25×9&lt;sup&gt;''n''&lt;/sup&gt;+10×3&lt;sup&gt;''n''&lt;/sup&gt;+4)
* The base 16 family {C}D: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;+1)/5 and can be factored as (2×4&lt;sup&gt;''n''&lt;/sup&gt;−2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (2×4&lt;sup&gt;''n''&lt;/sup&gt;+2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) / 5
* The base 14 family 8{D}: Can be written as 9×14&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 12 family {B}9B: Can be written as 12&lt;sup&gt;''n''&lt;/sup&gt;−25, it is divisible by 13 if ''n'' is odd and can be factored as (12&lt;sup&gt;''n''/2&lt;/sup&gt;−5) × (12&lt;sup&gt;''n''/2&lt;/sup&gt;+5) if ''n'' is even
* The base 14 family {D}5: Can be written as 14&lt;sup&gt;''n''&lt;/sup&gt;−9, it is divisible by 5 if ''n'' is odd and can be factored as (14&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (14&lt;sup&gt;''n''/2&lt;/sup&gt;+3) if ''n'' is even
* The base 17 family 1{9}: Can be written as (25×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 17 family 7{9}: Can be written as (121×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 19 family 1{6}: Can be written as (4×19&lt;sup&gt;''n''&lt;/sup&gt;−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;+1) / 3 if ''n'' is even
* The base 24 family 3{N}: Can be written as 4×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 24 family 5{N}: Can be written as 6×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;−1) × (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;+1) if ''n'' is odd

If the conjecture above is true, then the [[:w:Sierpiński number|Sierpiński conjecture]] and [[:w:Riesel number|Riesel conjecture]] are also true, and the [https://www.mersenneforum.org/showthread.php?t=10761 dual Sierpiński conjecture] and the [https://www.mersenneforum.org/showthread.php?t=6545 dual Riesel conjecture] are also true, and the [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm Riesel conjectures] in all bases ''b'' are also true, and the [http://www.noprimeleftbehind.net/crus/SNOB-Sierp-conjectures.htm real Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Real-Riesel-conjectures.htm real Riesel conjectures] are also true, also, if the Athena conjecture is true, then there are infinitely many primes of these forms for fixed bases ''b'' ≥ 2 and variable exponents ''n'':

* (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) for all bases ''b'' which are not [[:w:Perfect power|perfect power]]s (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 for all odd bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''+1) for all bases ''b'' which are neither of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 nor of the form 4×''m''&lt;sup&gt;4&lt;/sup&gt; (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for prime bases ''b'': https://oeis.org/A065507)
* ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) for all bases ''b'' &gt; 2 (reference of this form: https://oeis.org/A243404)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591)
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 140324348, not == 1 mod 3
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 7, not == 34 mod 35
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 5, not == 34 mod 35, not of the form 6×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' &lt; 9162668342, not == 1 mod 3
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3, not == 20 mod 21, not == 47, 83 mod 195, not == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815, not == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615, ..., not [[:w:Cube (algebra)|cube]]s
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 7, not == 20 mod 21, not == 83, 307 mod 455, not == 1266, 13593, 27292, 46353 mod 63973, ..., not [[:w:Cube (algebra)|cube]]s
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 177744, not == 1 mod 5
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 4 mod 5, not [[:w:Square number|square]]s
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 11, not == 32 mod 33 (references of this form: https://oeis.org/A088782)
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 32 mod 33
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' not == 1 mod 3, not == 14 mod 15
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 1 mod 5, not == 14 mod 15, not of the form 11×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 13, not == 142 mod 143, not == 562, 828, 900, 1166 mod 1729, not == 597, 1143 mod 1885, not == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019, not == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705, ...
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 11, not == 142 mod 143, not == 307, 1143 mod 1595, not == 901, 6016, 7479, 18457 mod 19019, ...
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 for all odd bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 for all odd bases ''b'' (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+4 for all odd bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−4 for all odd bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139)
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3 (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PP.htm, http://www.bitman.name/math/table/474, https://pzktupel.de/Primetables/TableWilliams4.php)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PM.htm, http://www.bitman.name/math/table/471, https://pzktupel.de/Primetables/TableWilliams3.php)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''+1) for all bases ''b'' not == 1 mod 3 (references of this form: http://www.bitman.name/math/table/801, https://pzktupel.de/Primetables/TableWilliams8.php, https://oeis.org/A346149, https://oeis.org/A346154)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''+1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/798, https://pzktupel.de/Primetables/TableWilliams7.php, https://oeis.org/A178250)

By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes &gt; ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3&lt;sub&gt;592197&lt;/sub&gt;A, its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored).

The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]].

To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1 we only used it to sieve the sequence ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'', but 2 may not divide (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)).

Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates.

For the primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for the &quot;easy&quot; bases (bases ''b'' with ≤ 150 primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; (base ''b'' = 26 has 83 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 3 unsolved families, base ''b'' = 36 has 75 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 4 unsolved families, base ''b'' = 17 has 99 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 18 unsolved families, base ''b'' = 21 has 80 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 12 unsolved families, base ''b'' = 19 has 201 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation.

Currently, the final goal of the Athena problem project is finding the Athena set (i.e. finding all Athena primes) and proving that this set is exactly the Athena set (i.e. proving that these are all Athena primes (including the primality proving for the probable primes)) in all bases 2 ≤ ''b'' ≤ 36, i.e. solving all families in all bases 2 ≤ ''b'' ≤ 36. Solving all (unsolved) families in all bases 2 ≤ ''b'' ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ ''b'' ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a ''probable'' prime for many of them (since the smallest prime in a family may be too large (&gt; 10&lt;sup&gt;25000&lt;/sup&gt;) to be proved primality, unless its *N*−1 or/and *N*+1 can be ≥ 25% factored).

== Data ==

These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]] (Brillhart-Lehmer-Selfridge primality test), all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]])

The Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored:

* the 3176th Athena prime in base 13, 81010&lt;sub&gt;415&lt;/sub&gt;1, which equals 17746×13&lt;sup&gt;416&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&amp;open=ecm
* the 3177th Athena prime in base 13, 8110&lt;sub&gt;435&lt;/sub&gt;1, which equals 1366×13&lt;sup&gt;436&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&amp;open=ecm
* the 3188th Athena prime in base 13, 930&lt;sub&gt;1551&lt;/sub&gt;1, which equals 120×13&lt;sup&gt;1552&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&amp;open=ecm
* the 3191st Athena prime in base 13, 390&lt;sub&gt;6266&lt;/sub&gt;1, which equals 48×13&lt;sup&gt;6267&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&amp;open=ecm
* the 649th Athena prime in base 14, 34D&lt;sub&gt;708&lt;/sub&gt;, which equals 47×14&lt;sup&gt;708&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&amp;open=ecm
* the 650th Athena prime in base 14, 4D&lt;sub&gt;19698&lt;/sub&gt;, which equals 5×14&lt;sup&gt;19698&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&amp;open=ecm
* the 2335th Athena prime in base 16, 88F&lt;sub&gt;545&lt;/sub&gt;, which equals 137×16&lt;sup&gt;545&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&amp;open=ecm
* the 10317th Athena prime in base 17, 5A70&lt;sub&gt;274&lt;/sub&gt;1, which equals 1622×17&lt;sup&gt;275&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&amp;open=ecm
* the 10359th Athena prime in base 17, 9D0&lt;sub&gt;1067&lt;/sub&gt;1, which equals 166×17&lt;sup&gt;1068&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&amp;open=ecm
* the 10370th Athena prime in base 17, A0&lt;sub&gt;1355&lt;/sub&gt;1, which equals 10×17&lt;sup&gt;1356&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&amp;open=ecm
* the 10386th Athena prime in base 17, 530&lt;sub&gt;4867&lt;/sub&gt;1, which equals 88×17&lt;sup&gt;4868&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&amp;open=ecm
* the 10408th Athena prime in base 17, 570&lt;sub&gt;51310&lt;/sub&gt;1, which equals 92×17&lt;sup&gt;51311&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&amp;open=ecm
* the 10412th Athena prime in base 17, 970&lt;sub&gt;166047&lt;/sub&gt;1, which equals 160×17&lt;sup&gt;166048&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&amp;open=ecm
* the 10413th Athena prime in base 17, F70&lt;sub&gt;186767&lt;/sub&gt;1, which equals 262×17&lt;sup&gt;186768&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&amp;open=ecm
* the 3310th Athena prime in base 20, JCJ&lt;sub&gt;629&lt;/sub&gt;, which equals 393×20&lt;sup&gt;629&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&amp;open=ecm
* the 13373rd Athena prime in base 21, 5D0&lt;sub&gt;19848&lt;/sub&gt;1, which equals 118×21&lt;sup&gt;19849&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&amp;open=ecm
* the 3408th Athena prime in base 24, 88N&lt;sub&gt;5951&lt;/sub&gt;, which equals 201×24&lt;sup&gt;5951&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&amp;open=ecm
* the 25509th Athena prime in base 28, EB0&lt;sub&gt;405&lt;/sub&gt;1, which equals 403×28&lt;sup&gt;406&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&amp;open=ecm
* the 2616th Athena prime in base 30, C0&lt;sub&gt;1022&lt;/sub&gt;1, which equals 12×30&lt;sup&gt;1023&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&amp;open=ecm
* the 2619th Athena prime in base 30, OT&lt;sub&gt;34205&lt;/sub&gt;, which equals 25×30&lt;sup&gt;34205&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&amp;open=ecm
* the 35237th Athena prime in base 36, P8Z&lt;sub&gt;390&lt;/sub&gt;, which equals 909×36&lt;sup&gt;390&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&amp;open=ecm

and the Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') = (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1), &quot;''S''&lt;sub&gt;''n''&lt;/sub&gt;(''b'')&quot; means ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)

* the 3168th Athena prime in base 13, 9&lt;sub&gt;308&lt;/sub&gt;1, ''N''−1 is 117×''R''&lt;sub&gt;308&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;308&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=308&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=308&amp;c0=-&amp;EN=&amp;LM=
* the 3179th Athena prime in base 13, B&lt;sub&gt;563&lt;/sub&gt;C, ''N''−1 is 11×''R''&lt;sub&gt;564&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;564&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=564&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=564&amp;c0=-&amp;EN=&amp;LM=
* the 3180th Athena prime in base 13, 1B&lt;sub&gt;576&lt;/sub&gt;, ''N''−1 is 23×''R''&lt;sub&gt;576&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;576&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=576&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=576&amp;c0=-&amp;EN=&amp;LM=
* the 10320th Athena prime in base 17, 9&lt;sub&gt;292&lt;/sub&gt;1, ''N''−1 is 153×''R''&lt;sub&gt;292&lt;/sub&gt;(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17&lt;sup&gt;292&lt;/sup&gt;−1, and for the algebraic factors of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&amp;Exp=292&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&amp;Exp=292&amp;c0=-&amp;EN=&amp;LM=
* the 13304th Athena prime in base 21, 7&lt;sub&gt;230&lt;/sub&gt;1, ''N''−1 is 147×''R''&lt;sub&gt;230&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;230&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=230&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=230&amp;c0=-&amp;EN=&amp;LM=
* the 13355th Athena prime in base 21, 3&lt;sub&gt;1063&lt;/sub&gt;2, ''N''+1 is 3×''R''&lt;sub&gt;1064&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;1064&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=1064&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=1064&amp;c0=-&amp;EN=&amp;LM=
* the 25199th Athena prime in base 26, 9K&lt;sub&gt;343&lt;/sub&gt;AP, ''N''+1 is 6370×''R''&lt;sub&gt;344&lt;/sub&gt;(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26&lt;sup&gt;344&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=344&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=344&amp;c0=-&amp;EN=&amp;LM=
* the 25200th Athena prime in base 26, 8&lt;sub&gt;354&lt;/sub&gt;1, ''N''−1 is 208×''R''&lt;sub&gt;354&lt;/sub&gt;(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26&lt;sup&gt;354&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=354&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=354&amp;c0=-&amp;EN=&amp;LM=

All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], &quot;{}&quot; means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 means 123333567 (all subscripts are written in decimal).

Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11}

Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111}

Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221}

Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10&lt;sub&gt;93&lt;/sub&gt;13, and its algebraic form is 5&lt;sup&gt;95&lt;/sup&gt;+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013}

Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041}

Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3&lt;sub&gt;16&lt;/sub&gt;1, and its algebraic form is (7&lt;sup&gt;17&lt;/sup&gt;−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331}

Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4&lt;sub&gt;220&lt;/sub&gt;7, and its algebraic form is (4×8&lt;sup&gt;221&lt;/sup&gt;+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447}

Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30&lt;sub&gt;1158&lt;/sub&gt;11, and its algebraic form is 3×9&lt;sup&gt;1160&lt;/sup&gt;+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011}

Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50&lt;sub&gt;28&lt;/sub&gt;27, and its algebraic form is 5×10&lt;sup&gt;30&lt;/sup&gt;+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57&lt;sub&gt;62668&lt;/sub&gt;), the largest of which has 62669 digits (it is 57&lt;sub&gt;62668&lt;/sub&gt;, and its algebraic form is (57×11&lt;sup&gt;62668&lt;/sup&gt;−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11]

Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40&lt;sub&gt;39&lt;/sub&gt;77, and its algebraic form is 4×12&lt;sup&gt;41&lt;/sup&gt;+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077}

Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5&lt;sub&gt;23755&lt;/sub&gt;C, 80&lt;sub&gt;32017&lt;/sub&gt;111, 95&lt;sub&gt;197420&lt;/sub&gt;, A3&lt;sub&gt;592197&lt;/sub&gt;A), the largest of which has 592199 digits (it is A3&lt;sub&gt;592197&lt;/sub&gt;A, and its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13]

Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D&lt;sub&gt;19698&lt;/sub&gt;, and its algebraic form is 5×14&lt;sup&gt;19698&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14]

Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7&lt;sub&gt;155&lt;/sub&gt;97, and its algebraic form is (15&lt;sup&gt;157&lt;/sup&gt;+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15]

Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB&lt;sub&gt;32234&lt;/sub&gt;, 4&lt;sub&gt;72785&lt;/sub&gt;DD, 3&lt;sub&gt;116137&lt;/sub&gt;AF), the largest of which has 116139 digits (it is 3&lt;sub&gt;116137&lt;/sub&gt;AF, and its algebraic form is (16&lt;sup&gt;116139&lt;/sup&gt;+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16]

Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17]

Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0&lt;sub&gt;6268&lt;/sub&gt;C5, and its algebraic form is 12×18&lt;sup&gt;6270&lt;/sup&gt;+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18]

Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19]

Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0&lt;sub&gt;6269&lt;/sub&gt;D, and its algebraic form is 16×20&lt;sup&gt;6270&lt;/sup&gt;+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20]

Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21]

Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK&lt;sub&gt;22001&lt;/sub&gt;5), the largest of which has 22003 digits (it is BK&lt;sub&gt;22001&lt;/sub&gt;5, and its algebraic form is (251×22&lt;sup&gt;22002&lt;/sup&gt;−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22]

Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23]

Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N&lt;sub&gt;8129&lt;/sub&gt;LN, and its algebraic form is 13249×24&lt;sup&gt;8131&lt;/sup&gt;−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24]

Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25]

Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5&lt;sub&gt;19391&lt;/sub&gt;6F, 7&lt;sub&gt;20279&lt;/sub&gt;OL, LD0&lt;sub&gt;20975&lt;/sub&gt;7, 6K&lt;sub&gt;23300&lt;/sub&gt;5, J0&lt;sub&gt;44303&lt;/sub&gt;KCB, M0&lt;sub&gt;61186&lt;/sub&gt;2BB, 85M&lt;sub&gt;197060&lt;/sub&gt;B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26]

Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27]

Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6&lt;sub&gt;24051&lt;/sub&gt;LR, 5OA&lt;sub&gt;31238&lt;/sub&gt;F, O4O&lt;sub&gt;94535&lt;/sub&gt;9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28]

Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29]

Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0&lt;sub&gt;24608&lt;/sub&gt;D), the largest of which has 34206 digits (it is OT&lt;sub&gt;34205&lt;/sub&gt;, and its algebraic form is 25×30&lt;sup&gt;34205&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30]

Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31]

Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32]

Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33]

Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34]

Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35]

Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K&lt;sub&gt;26567&lt;/sub&gt;Z, S0&lt;sub&gt;75007&lt;/sub&gt;8H, P&lt;sub&gt;81993&lt;/sub&gt;SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36]

== Condensed table for bases 2 ≤ ''b'' ≤ 36 ==

{|class=&quot;wikitable&quot;
||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write &quot;''d''&lt;sub&gt;''n''&lt;/sub&gt;&quot; if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)||
|-
||2||1||11||2||1||3||http://factordb.com/index.php?id=3&amp;open=ecm||http://factordb.com/index.php?showid=3&amp;base=2||0||–||
|-
||3||3||111&lt;br&gt;21&lt;br&gt;12||3&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;1&lt;br&gt;1||13&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=13&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=3&lt;nowiki/&gt;||0||–||
|-
||4||5||221&lt;br&gt;31&lt;br&gt;23&lt;br&gt;13&lt;br&gt;11||3&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;1&lt;br&gt;1||41&lt;br&gt;13&lt;br&gt;11&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=41&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=41&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=4&lt;nowiki/&gt;||0||–||
|-
||5||22||10&lt;sub&gt;93&lt;/sub&gt;13&lt;br&gt;300031&lt;br&gt;44441&lt;br&gt;33331&lt;br&gt;33001&lt;br&gt;30301&lt;br&gt;14444&lt;br&gt;10103&lt;br&gt;3101&lt;br&gt;414||96&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4&lt;br&gt;3||67&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;3&lt;br&gt;3&lt;br&gt;3||5&lt;sup&gt;95&lt;/sup&gt;+8&lt;br&gt;9391&lt;br&gt;3121&lt;br&gt;2341&lt;br&gt;2251&lt;br&gt;1951&lt;br&gt;1249&lt;br&gt;653&lt;br&gt;401&lt;br&gt;109||http://factordb.com/index.php?id=1100000000034686071&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9391&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=3121&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2341&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2251&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1951&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1249&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=653&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=401&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=109&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000000034686071&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=9391&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=3121&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2341&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2251&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1951&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1249&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=653&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=401&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=109&amp;base=5&lt;nowiki/&gt;||0||–||
|-
||6||11||40041&lt;br&gt;4441&lt;br&gt;4401&lt;br&gt;51&lt;br&gt;45&lt;br&gt;35&lt;br&gt;31&lt;br&gt;25&lt;br&gt;21&lt;br&gt;15||5&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||5209&lt;br&gt;1033&lt;br&gt;1009&lt;br&gt;31&lt;br&gt;29&lt;br&gt;23&lt;br&gt;19&lt;br&gt;17&lt;br&gt;13&lt;br&gt;11||http://factordb.com/index.php?id=5209&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1033&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1009&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=31&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=29&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=23&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=19&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=17&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=5209&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1033&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1009&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=31&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=29&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=23&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=19&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=17&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=6&lt;nowiki/&gt;||0||–||
|-
||7||71||3&lt;sub&gt;16&lt;/sub&gt;1&lt;br&gt;510&lt;sub&gt;7&lt;/sub&gt;1&lt;br&gt;3&lt;sub&gt;6&lt;/sub&gt;01&lt;br&gt;1100021&lt;br&gt;531101&lt;br&gt;351101&lt;br&gt;300053&lt;br&gt;150001&lt;br&gt;100121&lt;br&gt;40054||17&lt;br&gt;10&lt;br&gt;8&lt;br&gt;7&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;5||15&lt;br&gt;9&lt;br&gt;7&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4||(7&lt;sup&gt;17&lt;/sup&gt;−5)/2&lt;br&gt;36×7&lt;sup&gt;8&lt;/sup&gt;+1&lt;br&gt;(7&lt;sup&gt;8&lt;/sup&gt;−47)/2&lt;br&gt;134471&lt;br&gt;91631&lt;br&gt;62819&lt;br&gt;50459&lt;br&gt;28813&lt;br&gt;16871&lt;br&gt;9643||http://factordb.com/index.php?id=116315256993601&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=207532837&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2882377&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=134471&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=91631&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=62819&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=50459&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=28813&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=16871&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9643&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=116315256993601&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=207532837&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=2882377&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=134471&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=91631&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=62819&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=50459&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=28813&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=16871&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=9643&amp;base=7&lt;nowiki/&gt;||0||–||
|-
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||33||280012~280093||DP&lt;sub&gt;95093&lt;/sub&gt;M5&lt;br&gt;HJ0&lt;sub&gt;94295&lt;/sub&gt;J&lt;br&gt;90&lt;sub&gt;93597&lt;/sub&gt;Q&lt;br&gt;9F0&lt;sub&gt;93157&lt;/sub&gt;N&lt;br&gt;7&lt;sub&gt;89449&lt;/sub&gt;333H&lt;br&gt;K3&lt;sub&gt;80751&lt;/sub&gt;6K&lt;br&gt;D&lt;sub&gt;80107&lt;/sub&gt;9UD&lt;br&gt;VFU&lt;sub&gt;72204&lt;/sub&gt;FK&lt;br&gt;J&lt;sub&gt;68715&lt;/sub&gt;2BJ&lt;br&gt;DF0&lt;sub&gt;68367&lt;/sub&gt;J||95096&lt;br&gt;94298&lt;br&gt;93599&lt;br&gt;93160&lt;br&gt;89453&lt;br&gt;80754&lt;br&gt;80110&lt;br&gt;72208&lt;br&gt;68718&lt;br&gt;68370||144405&lt;br&gt;143193&lt;br&gt;142131&lt;br&gt;141465&lt;br&gt;135835&lt;br&gt;122626&lt;br&gt;121648&lt;br&gt;109649&lt;br&gt;104350&lt;br&gt;103821||(441×33&lt;sup&gt;95095&lt;/sup&gt;−3833)/32&lt;br&gt;580×33&lt;sup&gt;94296&lt;/sup&gt;+19&lt;br&gt;9×33&lt;sup&gt;93598&lt;/sup&gt;+26&lt;br&gt;312×33&lt;sup&gt;93158&lt;/sup&gt;+23&lt;br&gt;(7×33&lt;sup&gt;89453&lt;/sup&gt;−4743239)/32&lt;br&gt;(643×33&lt;sup&gt;80753&lt;/sup&gt;+3709)/32&lt;br&gt;(13×33&lt;sup&gt;80110&lt;/sup&gt;−121453)/32&lt;br&gt;(16623×33&lt;sup&gt;72206&lt;/sup&gt;−8095)/16&lt;br&gt;(19×33&lt;sup&gt;68718&lt;/sup&gt;−600883)/32&lt;br&gt;444×33&lt;sup&gt;68368&lt;/sup&gt;+19||http://factordb.com/index.php?id=1100000005652348775&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652362811&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652375073&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652389776&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652430746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652446200&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652461592&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614764298&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614770536&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614784274&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000005652348775&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652362811&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652375073&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652389776&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652430746&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652446200&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652461592&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614764298&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614770536&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614784274&amp;base=33&lt;nowiki/&gt;||81||100000||
|-
||34||184785~184832||GFGC&lt;sub&gt;99996&lt;/sub&gt;5&lt;br&gt;90&lt;sub&gt;97950&lt;/sub&gt;FJ&lt;br&gt;NM0&lt;sub&gt;85218&lt;/sub&gt;KX&lt;br&gt;F&lt;sub&gt;83189&lt;/sub&gt;H2HP&lt;br&gt;P&lt;sub&gt;79441&lt;/sub&gt;444P&lt;br&gt;6&lt;sub&gt;77027&lt;/sub&gt;8X&lt;br&gt;XQIQ&lt;sub&gt;72241&lt;/sub&gt;D&lt;br&gt;T&lt;sub&gt;66530&lt;/sub&gt;IF&lt;br&gt;4&lt;sub&gt;66152&lt;/sub&gt;B&lt;br&gt;2EEC&lt;sub&gt;66039&lt;/sub&gt;7||100000&lt;br&gt;97953&lt;br&gt;85222&lt;br&gt;83193&lt;br&gt;79445&lt;br&gt;77029&lt;br&gt;72245&lt;br&gt;66532&lt;br&gt;66153&lt;br&gt;66043||153148&lt;br&gt;150013&lt;br&gt;130516&lt;br&gt;127408&lt;br&gt;121669&lt;br&gt;117968&lt;br&gt;110642&lt;br&gt;101893&lt;br&gt;101312&lt;br&gt;101143||(209246×34&lt;sup&gt;99997&lt;/sup&gt;−81)/11&lt;br&gt;9×34&lt;sup&gt;97952&lt;/sup&gt;+529&lt;br&gt;804×34&lt;sup&gt;85220&lt;/sup&gt;+713&lt;br&gt;(5×34&lt;sup&gt;83193&lt;/sup&gt;+700233)/11&lt;br&gt;(25×34&lt;sup&gt;79445&lt;/sup&gt;−28062367)/33&lt;br&gt;(2×34&lt;sup&gt;77029&lt;/sup&gt;+1043)/11&lt;br&gt;(1288676×34&lt;sup&gt;72242&lt;/sup&gt;−455)/33&lt;br&gt;(29×34&lt;sup&gt;66532&lt;/sup&gt;−12833)/33&lt;br&gt;(4×34&lt;sup&gt;66153&lt;/sup&gt;+227)/33&lt;br&gt;(30826×34&lt;sup&gt;66040&lt;/sup&gt;−59)/11||http://factordb.com/index.php?id=1100000004702891268&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702894713&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702900996&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702910376&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702913746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702918600&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399656529&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399657696&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399658651&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399659716&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000004702891268&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702894713&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702900996&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702910376&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702913746&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702918600&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399656529&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399657696&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399658651&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399659716&amp;base=34&lt;nowiki/&gt;||47||100000||
|-
||35||720002~720062||N0N&lt;sub&gt;99971&lt;/sub&gt;9&lt;br&gt;V0&lt;sub&gt;83669&lt;/sub&gt;E73&lt;br&gt;N&lt;sub&gt;81563&lt;/sub&gt;K7N&lt;br&gt;BJ0&lt;sub&gt;81279&lt;/sub&gt;N&lt;br&gt;J0&lt;sub&gt;80062&lt;/sub&gt;FUH&lt;br&gt;43V&lt;sub&gt;79754&lt;/sub&gt;&lt;br&gt;9&lt;sub&gt;76600&lt;/sub&gt;K3&lt;br&gt;LB&lt;sub&gt;71366&lt;/sub&gt;PB&lt;br&gt;Q&lt;sub&gt;64150&lt;/sub&gt;H&lt;br&gt;50&lt;sub&gt;63397&lt;/sub&gt;5R||99974&lt;br&gt;83673&lt;br&gt;81566&lt;br&gt;81282&lt;br&gt;80066&lt;br&gt;79756&lt;br&gt;76602&lt;br&gt;71369&lt;br&gt;64151&lt;br&gt;63400||154367&lt;br&gt;129197&lt;br&gt;125944&lt;br&gt;125505&lt;br&gt;123628&lt;br&gt;123148&lt;br&gt;118279&lt;br&gt;110199&lt;br&gt;99054&lt;br&gt;97894||(27393×35&lt;sup&gt;99972&lt;/sup&gt;−499)/34&lt;br&gt;31×35&lt;sup&gt;83672&lt;/sup&gt;+17398&lt;br&gt;(23×35&lt;sup&gt;81566&lt;/sup&gt;−144013)/34&lt;br&gt;404×35&lt;sup&gt;81280&lt;/sup&gt;+23&lt;br&gt;19×35&lt;sup&gt;80065&lt;/sup&gt;+19442&lt;br&gt;(4893×35&lt;sup&gt;79754&lt;/sup&gt;−31)/34&lt;br&gt;(9×35&lt;sup&gt;76602&lt;/sup&gt;+12877)/34&lt;br&gt;(725×35&lt;sup&gt;71368&lt;/sup&gt;+16649)/34&lt;br&gt;(13×35&lt;sup&gt;64151&lt;/sup&gt;−166)/17&lt;br&gt;5×35&lt;sup&gt;63399&lt;/sup&gt;+202||http://factordb.com/index.php?id=1100000008248342445&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248353306&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248375642&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248397018&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248412468&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248418540&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248423670&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192119974&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192126630&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192129294&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000008248342445&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248353306&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248375642&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248397018&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248412468&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248418540&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248423670&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192119974&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192126630&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192129294&amp;base=35&lt;nowiki/&gt;||60||100000||
|-
||36||35286~35290||P&lt;sub&gt;81993&lt;/sub&gt;SZ&lt;br&gt;S0&lt;sub&gt;75007&lt;/sub&gt;8H&lt;br&gt;7K&lt;sub&gt;26567&lt;/sub&gt;Z&lt;br&gt;J&lt;sub&gt;10117&lt;/sub&gt;LJ&lt;br&gt;VL0&lt;sub&gt;7258&lt;/sub&gt;J&lt;br&gt;EO0&lt;sub&gt;6177&lt;/sub&gt;V&lt;br&gt;FZ&lt;sub&gt;5777&lt;/sub&gt;3P&lt;br&gt;T09&lt;sub&gt;4618&lt;/sub&gt;1&lt;br&gt;RY&lt;sub&gt;4562&lt;/sub&gt;H&lt;br&gt;OZ&lt;sub&gt;3932&lt;/sub&gt;AZ||81995&lt;br&gt;75010&lt;br&gt;26569&lt;br&gt;10119&lt;br&gt;7261&lt;br&gt;6180&lt;br&gt;5780&lt;br&gt;4621&lt;br&gt;4564&lt;br&gt;3935||127609&lt;br&gt;116739&lt;br&gt;41349&lt;br&gt;15748&lt;br&gt;11301&lt;br&gt;9618&lt;br&gt;8996&lt;br&gt;7192&lt;br&gt;7103&lt;br&gt;6124||(5×36&lt;sup&gt;81995&lt;/sup&gt;+821)/7&lt;br&gt;28×36&lt;sup&gt;75009&lt;/sup&gt;+305&lt;br&gt;(53×36&lt;sup&gt;26568&lt;/sup&gt;+101)/7&lt;br&gt;(19×36&lt;sup&gt;10119&lt;/sup&gt;+2501)/35&lt;br&gt;1137×36&lt;sup&gt;7259&lt;/sup&gt;+19&lt;br&gt;528×36&lt;sup&gt;6178&lt;/sup&gt;+31&lt;br&gt;16×36&lt;sup&gt;5779&lt;/sup&gt;−1163&lt;br&gt;(36549×36&lt;sup&gt;4619&lt;/sup&gt;−289)/35&lt;br&gt;(979×36&lt;sup&gt;4563&lt;/sup&gt;−629)/35&lt;br&gt;25×36&lt;sup&gt;3934&lt;/sup&gt;−901||http://factordb.com/index.php?id=1100000002394962083&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004020085177&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003896952461&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362491&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362489&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362488&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362487&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362486&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362485&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000000840634476&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000002394962083&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000004020085177&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003896952461&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362491&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362489&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362488&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362487&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362486&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362485&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000000840634476&amp;base=36&lt;nowiki/&gt;||4||200000||
|}

== The fully proof of Athena problem in decimal (base ''b'' = 10) ==

'''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''.

Assume ''p'' is a prime &gt; 10, and the last digit of ''p'' must lie in {1,3,7,9}.

Case 1: ''p'' ends with 1.

In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9.

Case 1.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''.

If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''.

Case 1.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8.

If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}.

If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''.

If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite.

Case 1.3: ''p'' begins with 8.

In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5.

If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}.

If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element.

Case 1.4: ''p'' begins with 9.

In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8.

If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8.

If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}.

If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801.

Case 2: ''p'' ends with 3.

In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 3: ''p'' ends with 7.

In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8.

Case 3.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8.

If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}.

If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40&lt;sub&gt;''n''&lt;/sub&gt;1 = 280&lt;sub&gt;''n''&lt;/sub&gt;7.

Case 3.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''.

If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''.

Case 3.3: ''p'' begins with 7.

In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime.

Case 3.4: ''p'' begins with 8.

In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 4: ''p'' ends with 9.

In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9.

If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's.

If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4.

Case 4.1: ''p'' begins with 3.

In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''.

Case 4.2: ''p'' begins with 4.

In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6&lt;sub&gt;''n''&lt;/sub&gt;7 = 46&lt;sub&gt;''n''&lt;/sub&gt;9.

Case 4.3: ''p'' begins with 6.

In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty.

If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6.

If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}.

If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes.

Case 4.4: ''p'' begins with 9.

In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty.

If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669.

[[Category:Number theory]]</text>
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    <revision>
      <id>2833721</id>
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        <username>Athene241</username>
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      <text bytes="158879" sha1="3c94qeadb4el3q9zx00k04ezcugoq7h" xml:space="preserve">{{mathematics}}
'''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' &gt; 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the &quot;[[:w:Prime number|prime number]] [[:w:Greater than|&gt;]] ''b''&quot; [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, &quot;string&quot; is a subsequence of &quot;meistersinger&quot;. In contrast, 758 is not a subsequence of 378259, &quot;abc&quot; is not a subsequence of &quot;cbacacba&quot;, since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]])

Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|&gt;]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''&lt;sub&gt;''b''&lt;/sub&gt; := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' &gt; 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''.

By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}.

Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers &gt; ''b'', whose set is exactly the Athena set in base ''b'').

Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''&lt;sub&gt;''b''&lt;/sub&gt;) (i.e. to compute the Athena set in base ''b''), where ''L''&lt;sub&gt;''b''&lt;/sub&gt; is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|&gt;]] ''b'', for 2 ≤ ''b'' ≤ 36.

For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes &gt; ''b'' or probable primes &gt; ''b'' with length ≤ 100000. (The chance that an unproven probable prime in these sets is in fact composite is less than 10&lt;sup&gt;−2000&lt;/sup&gt;, see https://t5k.org/notes/prp_prob.html)

Below, family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') means sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), where the members are expressed as base ''b'' strings, like the numbers in https://stdkmd.net/nrr/aaaab.htm, https://stdkmd.net/nrr/abbbb.htm, https://stdkmd.net/nrr/aaaba.htm, https://stdkmd.net/nrr/abaaa.htm, https://stdkmd.net/nrr/abbba.htm, https://stdkmd.net/nrr/abbbc.htm, e.g. 1{3} (in decimal) is the numbers in https://stdkmd.net/nrr/1/13333.htm#about_first, and {1}3 (in decimal) is the numbers in https://stdkmd.net/nrr/1/11113.htm#about_first, and 31{3} (in decimal) is the numbers in https://stdkmd.net/nrr/3/31333.htm#about_first, and {1}31 (in decimal) is the numbers in https://stdkmd.net/nrr/1/11131.htm#about_first, and 1{2}3 (in decimal) is the numbers in https://stdkmd.net/nrr/1/12223.htm#about_first, also, superscripts always means exponents, subscripts are always used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 = 123333567, all subscripts are written in decimal.

== Solve the problem ==

To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime &gt; ''b'' in all such families.

We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') &quot;linear&quot; families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows:

* 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''.
* 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by:
* 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''.
* 2.2. If possible, simplify the family.
* 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers &gt; ''b''), and if so then remove the family from ''L''.
* 3. Update ''L'', after each split examine the new families as in step 2.

e.g. in decimal (base ''b'' = 10):

''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991}

''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9}

and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1

and since the family 2{0}1 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1

221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L''

none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L''

and since the family 3{0,3,6,9}3 can be proven to contain no primes &gt; base (since all numbers in this family are divisible by 3), it can be removed

etc.

Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime &gt; ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime &gt; ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime &gt; ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both &quot;numbers of Athena primes in base ''b''&quot; and &quot;length of the largest Athena prime in base ''b''&quot; are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;.

Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'')

* If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and the string ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and both the strings ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' and ''xy''&lt;sub&gt;2&lt;/sub&gt;''y''&lt;sub&gt;1&lt;/sub&gt;''z'' represent a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}''z'' ∪ ''x''{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.

e.g. in decimal (base ''b'' = 10):

* 2221 is a prime &gt; 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
* 227 is a prime &gt; 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
* 449 is a prime &gt; 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
* Both 5051 and 5501 are primes &gt; 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
* 8501 is a prime &gt; 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
* 887 is a prime &gt; 10, and it is a subsequence of 2887, also 2087 is a prime &gt; 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
* 349 and 449 are primes &gt; 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes &gt; 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
* 251, 281, 521, 821, 881 are primes &gt; 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes &gt; 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''&lt;sub&gt;1&lt;/sub&gt;, ''y''&lt;sub&gt;2&lt;/sub&gt;, ..., ''y''&lt;sub&gt;''n''&lt;/sub&gt;}, then we can replace ''x''{''Y''}''z'' by ''xy''&lt;sub&gt;1&lt;/sub&gt;{''Y''}''z'' ∪ ''xy''&lt;sub&gt;2&lt;/sub&gt;{''Y''}''z'' ∪ ... ∪ ''xy''&lt;sub&gt;''n''&lt;/sub&gt;{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]].

If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base ''b'' = 10):

* The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
* The smallest prime in the family {5}1 is 555555555551.
* The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'').

The following is a &quot;[[:w:Semi-algorithm|semi-algorithm]]&quot; that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement:

# ''M'' = ''[[:w:Empty string|∅]]''
# while (''L'' ≠ ''∅'') do
# choose ''x'', a shortest string in ''L''
# ''M'' := ''M'' ∪ {''x''}
# ''L'' := ''L'' − ''sup''({''x''})

In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&amp;#39;, some regular overapproximation to ''L'', until we can show ''L''&amp;#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&amp;#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''&lt;sub&gt;1&lt;/sub&gt;{''L''&lt;sub&gt;2&lt;/sub&gt;}''L''&lt;sub&gt;3&lt;/sub&gt;, where each of ''L''&lt;sub&gt;1&lt;/sub&gt;, ''L''&lt;sub&gt;2&lt;/sub&gt;, ''L''&lt;sub&gt;3&lt;/sub&gt; is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not.

Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''&lt;sup&gt;''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)&lt;/sup&gt;), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]).

To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime &gt; ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2&lt;sup&gt;''n''−2&lt;/sup&gt; strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length &gt; (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' &lt; ''b'', i.e. finding the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (or prove such prime does not exist) with ''k'' &lt; ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is &lt; ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist) (in fact, it is known that exactly what bases 2 ≤ ''b'' ≤ 1024 have the families listed in the table below as unsolved families, all of these families in all bases 2 ≤ ''b'' ≤ 1024 have been searched to length ≥ 10000 (for the family (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1), bases 2 ≤ ''b'' ≤ 1048576, searched to length ≥ 5000)): (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)):

'''Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' for some ''n'' ≥ 0?'''

An [[:w:Algorithm|algorithm]] to solve this problem, for example, would allow us to decide if there are any additional [[:w:Fermat prime|Fermat prime]]s other than the known ones (corresponding to ''n'' = 0, 1, 2, 3, 4). To see this, take ''b'' = 2, ''x'' = 1, ''y'' = 0, and ''z'' = 0&lt;sub&gt;16&lt;/sub&gt;1. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;+1 is prime then ''n'' must be a [[:w:Power of 2|power of two]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Fermat prime. Besides, it would allow us to decide if there are infinitely many [[:w:Mersenne prime|Mersenne prime]]s (of the form 2&lt;sup&gt;''p''&lt;/sup&gt;−1 with prime ''p''). To see this, take ''b'' = 2, ''x'' = ''𝜆'' (the [[:w:Empty string|empty string]]), ''y'' = 1, and ''z'' = 1&lt;sub&gt;''n''+1&lt;/sub&gt;, where ''n'' is the exponent of the Mersenne prime which we want to know whether it is the largest Mersenne prime or not. Since if 2&lt;sup&gt;''n''&lt;/sup&gt;−1 is prime then ''n'' must be a [[:w:Prime number|prime]], a prime of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' must be a new Mersenne prime. Also, it would allow us to decide whether 78557 is the smallest [[:w:Sierpinski number|Sierpinski number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;''n''&lt;/sup&gt;+1 is composite for all ''n'' ≥ 1) and whether 509203 is the smallest [[:w:Riesel number|Riesel number]] (i.e. odd numbers ''k'' such that ''k''×2&lt;sup&gt;*n*&lt;/sup&gt;−1 is composite for all ''n'' ≥ 1), etc.

'''Conjecture (this conjecture is very important for the Athena problem): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes).'''

(in fact, this conjecture is equivalent to the conjecture (to prove this, by change the base (''b'') to a power of ''b'' which is larger than the largest prime in a given family (in base ''b'') which only contains finitely many primes): If family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then family ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' in base ''b'' contains at least one prime (this is equivalent to: If form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) contains at least one prime), like the [[:w:Bunyakovsky conjecture|Bunyakovsky conjecture]] and the [[:w:Dickson's conjecture|Dickson's conjecture]] and the [[:w:Schinzel's hypothesis H|Schinzel's hypothesis ''H'']], if such ''n'' always exists, then there must be always infinitely many such ''n'', to prove this, add another polynomial for the cases of the Dickson's conjecture and the Schinzel's hypothesis ''H'', also, change the polynomial (e.g. change ''n'' to ''r''×''n'' or ''n''&lt;sup&gt;''r''&lt;/sup&gt; for all integers ''r'' &gt; 1) for the cases of the Bunyakovsky conjecture and the Schinzel's hypothesis ''H'')

Some families can be ruled out to contain no prime &gt; ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''&lt;sup&gt;4&lt;/sup&gt;+4×''y''&lt;sup&gt;4&lt;/sup&gt;]]), or combine of them, e.g.

* The base 9 family 2{7}: Always divisible by 2 or 5
* The base 11 family 2{5}: Always divisible by 2 or 3
* The base 14 family B{0}1: Always divisible by 3 or 5
* The base 13 family 95{0}3: Always divisible by 5, 7, or 17
* The base 16 family {4}D: Always divisible by 3, 7, or 13
* The base 16 family {8}F: Always divisible by 3, 7, or 13
* The base 21 family {7}D: Always divisible by 2, 13, or 17
* The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79
* The base 9 family {1}: Can be written as (9&lt;sup&gt;''n''&lt;/sup&gt;−1)/8 and can be factored as (3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 8
* The base 8 family 1{0}1: Can be written as 8&lt;sup&gt;''n''&lt;/sup&gt;+1 and can be factored as (2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (4&lt;sup&gt;''n''&lt;/sup&gt;−2&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 9 family 3{8}: Can be written as 4×9&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 16 family 1{5}: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−1)/3 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1) / 3
* The base 16 family {4}1: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−49)/15 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−7) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+7) / 15
* The base 27 family 7{Q}: Can be written as 8×27&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (4×9&lt;sup&gt;''n''&lt;/sup&gt;+2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 27 family 9{G}: Can be written as (125×27&lt;sup&gt;''n''&lt;/sup&gt;−8)/13 and can be factored as (5×3&lt;sup&gt;''n''&lt;/sup&gt;−2) × (25×9&lt;sup&gt;''n''&lt;/sup&gt;+10×3&lt;sup&gt;''n''&lt;/sup&gt;+4)
* The base 16 family {C}D: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;+1)/5 and can be factored as (2×4&lt;sup&gt;''n''&lt;/sup&gt;−2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (2×4&lt;sup&gt;''n''&lt;/sup&gt;+2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) / 5
* The base 14 family 8{D}: Can be written as 9×14&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 12 family {B}9B: Can be written as 12&lt;sup&gt;''n''&lt;/sup&gt;−25, it is divisible by 13 if ''n'' is odd and can be factored as (12&lt;sup&gt;''n''/2&lt;/sup&gt;−5) × (12&lt;sup&gt;''n''/2&lt;/sup&gt;+5) if ''n'' is even
* The base 14 family {D}5: Can be written as 14&lt;sup&gt;''n''&lt;/sup&gt;−9, it is divisible by 5 if ''n'' is odd and can be factored as (14&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (14&lt;sup&gt;''n''/2&lt;/sup&gt;+3) if ''n'' is even
* The base 17 family 1{9}: Can be written as (25×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 17 family 7{9}: Can be written as (121×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (11×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 19 family 1{6}: Can be written as (4×19&lt;sup&gt;''n''&lt;/sup&gt;−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;+1) / 3 if ''n'' is even
* The base 24 family 3{N}: Can be written as 4×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×24&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 24 family 5{N}: Can be written as 6×24&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;−1) × (12×24&lt;sup&gt;(''n''−1)/2&lt;/sup&gt;+1) if ''n'' is odd

If the conjecture above is true, then the [[:w:Sierpiński number|Sierpiński conjecture]] and [[:w:Riesel number|Riesel conjecture]] are also true, and the [https://www.mersenneforum.org/showthread.php?t=10761 dual Sierpiński conjecture] and the [https://www.mersenneforum.org/showthread.php?t=6545 dual Riesel conjecture] are also true, and the [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm Riesel conjectures] in all bases ''b'' are also true, and the [http://www.noprimeleftbehind.net/crus/SNOB-Sierp-conjectures.htm real Sierpiński conjectures] and the [http://www.noprimeleftbehind.net/crus/Real-Riesel-conjectures.htm real Riesel conjectures] are also true, also, if the Athena conjecture is true, then there are infinitely many primes of these forms for fixed bases ''b'' ≥ 2 and variable exponents ''n'':

* (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1) for all bases ''b'' which are not [[:w:Perfect power|perfect power]]s (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/2 for all odd bases ''b'' which are not of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 (for this form, ''n'' must be power of 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* (''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''+1) for all bases ''b'' which are neither of the form ''m''&lt;sup&gt;''r''&lt;/sup&gt; with odd ''r'' &gt; 1 nor of the form 4×''m''&lt;sup&gt;4&lt;/sup&gt; (for this form, ''n'' must be prime) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for prime bases ''b'': https://oeis.org/A065507)
* ((''b''−2)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)/(''b''−1) for all bases ''b'' &gt; 2 (reference of this form: https://oeis.org/A243404)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624)
* 2×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&amp;d=1567314217, https://oeis.org/A119591)
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 3×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* 4×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 140324348, not == 1 mod 3
* 5×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b''
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 7, not == 34 mod 35
* 6×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 5, not == 34 mod 35, not of the form 6×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b''
* 7×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' &lt; 9162668342, not == 1 mod 3
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3, not == 20 mod 21, not == 47, 83 mod 195, not == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815, not == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615, ..., not [[:w:Cube (algebra)|cube]]s
* 8×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 7, not == 20 mod 21, not == 83, 307 mod 455, not == 1266, 13593, 27292, 46353 mod 63973, ..., not [[:w:Cube (algebra)|cube]]s
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' &lt; 177744, not == 1 mod 5
* 9×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 4 mod 5, not [[:w:Square number|square]]s
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 11, not == 32 mod 33 (references of this form: https://oeis.org/A088782)
* 10×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 3, not == 32 mod 33
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all even bases ''b'' not == 1 mod 3, not == 14 mod 15
* 11×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all even bases ''b'' not == 1 mod 5, not == 14 mod 15, not of the form 11×''m''&lt;sup&gt;2&lt;/sup&gt; with ''m'' == 2, 3 mod 5
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 13, not == 142 mod 143, not == 562, 828, 900, 1166 mod 1729, not == 597, 1143 mod 1885, not == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019, not == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705, ...
* 12×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' not == 1 mod 11, not == 142 mod 143, not == 307, 1143 mod 1595, not == 901, 6016, 7479, 18457 mod 19019, ...
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+2 for all odd bases ''b'' &lt; 201446503145165177, not == 1 mod 3 (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−2 for all odd bases ''b'' (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−3 for all even bases ''b'' not divisible by 3
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+4 for all odd bases ''b'' not == 1 mod 5, not == 14 mod 15, not [[:w:Fourth power|fourth power]]s
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−4 for all odd bases ''b'' not == 1 mod 3, not == 4 mod 5, not [[:w:Square number|square]]s
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139)
* (''b''−1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 for all bases ''b'' not == 1 mod 3 (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PP.htm, http://www.bitman.name/math/table/474, https://pzktupel.de/Primetables/TableWilliams4.php)
* (''b''+1)×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 for all bases ''b'' (references of this form: http://www.noprimeleftbehind.net/Williams-primes-PM.htm, http://www.bitman.name/math/table/471, https://pzktupel.de/Primetables/TableWilliams3.php)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''−1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;+(''b''+1) for all bases ''b'' not == 1 mod 3 (references of this form: http://www.bitman.name/math/table/801, https://pzktupel.de/Primetables/TableWilliams8.php, https://oeis.org/A346149, https://oeis.org/A346154)
* ''b''&lt;sup&gt;''n''&lt;/sup&gt;−(''b''+1) for all bases ''b'' (references of this form: http://www.bitman.name/math/table/798, https://pzktupel.de/Primetables/TableWilliams7.php, https://oeis.org/A178250)

By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes &gt; ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3&lt;sub&gt;592197&lt;/sub&gt;A, its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored).

The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]].

To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1 we only used it to sieve the sequence ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'', but 2 may not divide (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)).

Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) &gt; 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates.

For the primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for the &quot;easy&quot; bases (bases ''b'' with ≤ 150 primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; (base ''b'' = 26 has 83 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 3 unsolved families, base ''b'' = 36 has 75 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 4 unsolved families, base ''b'' = 17 has 99 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 18 unsolved families, base ''b'' = 21 has 80 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 12 unsolved families, base ''b'' = 19 has 201 known primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation.

Currently, the final goal of the Athena problem project is finding the Athena set (i.e. finding all Athena primes) and proving that this set is exactly the Athena set (i.e. proving that these are all Athena primes (including the primality proving for the probable primes)) in all bases 2 ≤ ''b'' ≤ 36, i.e. solving all families in all bases 2 ≤ ''b'' ≤ 36. Solving all (unsolved) families in all bases 2 ≤ ''b'' ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ ''b'' ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a ''probable'' prime for many of them (since the smallest prime in a family may be too large (&gt; 10&lt;sup&gt;25000&lt;/sup&gt;) to be proved primality, unless its ''N''−1 or/and ''N''+1 can be ≥ 25% factored).

== Data ==

These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]] (Brillhart-Lehmer-Selfridge primality test), all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]])

The Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored:

* the 3176th Athena prime in base 13, 81010&lt;sub&gt;415&lt;/sub&gt;1, which equals 17746×13&lt;sup&gt;416&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&amp;open=ecm
* the 3177th Athena prime in base 13, 8110&lt;sub&gt;435&lt;/sub&gt;1, which equals 1366×13&lt;sup&gt;436&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&amp;open=ecm
* the 3188th Athena prime in base 13, 930&lt;sub&gt;1551&lt;/sub&gt;1, which equals 120×13&lt;sup&gt;1552&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&amp;open=ecm
* the 3191st Athena prime in base 13, 390&lt;sub&gt;6266&lt;/sub&gt;1, which equals 48×13&lt;sup&gt;6267&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&amp;open=ecm
* the 649th Athena prime in base 14, 34D&lt;sub&gt;708&lt;/sub&gt;, which equals 47×14&lt;sup&gt;708&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&amp;open=ecm
* the 650th Athena prime in base 14, 4D&lt;sub&gt;19698&lt;/sub&gt;, which equals 5×14&lt;sup&gt;19698&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&amp;open=ecm
* the 2335th Athena prime in base 16, 88F&lt;sub&gt;545&lt;/sub&gt;, which equals 137×16&lt;sup&gt;545&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&amp;open=ecm
* the 10317th Athena prime in base 17, 5A70&lt;sub&gt;274&lt;/sub&gt;1, which equals 1622×17&lt;sup&gt;275&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&amp;open=ecm
* the 10359th Athena prime in base 17, 9D0&lt;sub&gt;1067&lt;/sub&gt;1, which equals 166×17&lt;sup&gt;1068&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&amp;open=ecm
* the 10370th Athena prime in base 17, A0&lt;sub&gt;1355&lt;/sub&gt;1, which equals 10×17&lt;sup&gt;1356&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&amp;open=ecm
* the 10386th Athena prime in base 17, 530&lt;sub&gt;4867&lt;/sub&gt;1, which equals 88×17&lt;sup&gt;4868&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&amp;open=ecm
* the 10408th Athena prime in base 17, 570&lt;sub&gt;51310&lt;/sub&gt;1, which equals 92×17&lt;sup&gt;51311&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&amp;open=ecm
* the 10412th Athena prime in base 17, 970&lt;sub&gt;166047&lt;/sub&gt;1, which equals 160×17&lt;sup&gt;166048&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&amp;open=ecm
* the 10413th Athena prime in base 17, F70&lt;sub&gt;186767&lt;/sub&gt;1, which equals 262×17&lt;sup&gt;186768&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (&gt;10&lt;sup&gt;199999&lt;/sup&gt;) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&amp;open=ecm
* the 3310th Athena prime in base 20, JCJ&lt;sub&gt;629&lt;/sub&gt;, which equals 393×20&lt;sup&gt;629&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&amp;open=ecm
* the 13373rd Athena prime in base 21, 5D0&lt;sub&gt;19848&lt;/sub&gt;1, which equals 118×21&lt;sup&gt;19849&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&amp;open=ecm
* the 3408th Athena prime in base 24, 88N&lt;sub&gt;5951&lt;/sub&gt;, which equals 201×24&lt;sup&gt;5951&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&amp;open=ecm
* the 25509th Athena prime in base 28, EB0&lt;sub&gt;405&lt;/sub&gt;1, which equals 403×28&lt;sup&gt;406&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&amp;open=ecm
* the 2616th Athena prime in base 30, C0&lt;sub&gt;1022&lt;/sub&gt;1, which equals 12×30&lt;sup&gt;1023&lt;/sup&gt;+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&amp;open=ecm
* the 2619th Athena prime in base 30, OT&lt;sub&gt;34205&lt;/sub&gt;, which equals 25×30&lt;sup&gt;34205&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&amp;open=ecm
* the 35237th Athena prime in base 36, P8Z&lt;sub&gt;390&lt;/sub&gt;, which equals 909×36&lt;sup&gt;390&lt;/sup&gt;−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&amp;open=ecm

and the Athena primes &gt; 10&lt;sup&gt;299&lt;/sup&gt; in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''&lt;sub&gt;''n''&lt;/sub&gt;(''b'') = (''b''&lt;sup&gt;''n''&lt;/sup&gt;−1)/(''b''−1), &quot;''S''&lt;sub&gt;''n''&lt;/sub&gt;(''b'')&quot; means ''b''&lt;sup&gt;''n''&lt;/sup&gt;+1)

* the 3168th Athena prime in base 13, 9&lt;sub&gt;308&lt;/sub&gt;1, ''N''−1 is 117×''R''&lt;sub&gt;308&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;308&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=308&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;308&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=308&amp;c0=-&amp;EN=&amp;LM=
* the 3179th Athena prime in base 13, B&lt;sub&gt;563&lt;/sub&gt;C, ''N''−1 is 11×''R''&lt;sub&gt;564&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;564&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=564&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;564&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=564&amp;c0=-&amp;EN=&amp;LM=
* the 3180th Athena prime in base 13, 1B&lt;sub&gt;576&lt;/sub&gt;, ''N''−1 is 23×''R''&lt;sub&gt;576&lt;/sub&gt;(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13&lt;sup&gt;576&lt;/sup&gt;−1, and for the algebraic factors of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&amp;Exp=576&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 13&lt;sup&gt;576&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&amp;Exp=576&amp;c0=-&amp;EN=&amp;LM=
* the 10320th Athena prime in base 17, 9&lt;sub&gt;292&lt;/sub&gt;1, ''N''−1 is 153×''R''&lt;sub&gt;292&lt;/sub&gt;(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17&lt;sup&gt;292&lt;/sup&gt;−1, and for the algebraic factors of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&amp;Exp=292&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 17&lt;sup&gt;292&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&amp;Exp=292&amp;c0=-&amp;EN=&amp;LM=
* the 13304th Athena prime in base 21, 7&lt;sub&gt;230&lt;/sub&gt;1, ''N''−1 is 147×''R''&lt;sub&gt;230&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;230&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=230&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;230&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=230&amp;c0=-&amp;EN=&amp;LM=
* the 13355th Athena prime in base 21, 3&lt;sub&gt;1063&lt;/sub&gt;2, ''N''+1 is 3×''R''&lt;sub&gt;1064&lt;/sub&gt;(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21&lt;sup&gt;1064&lt;/sup&gt;−1, and for the algebraic factors of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&amp;Exp=1064&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 21&lt;sup&gt;1064&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&amp;Exp=1064&amp;c0=-&amp;EN=&amp;LM=
* the 25199th Athena prime in base 26, 9K&lt;sub&gt;343&lt;/sub&gt;AP, ''N''+1 is 6370×''R''&lt;sub&gt;344&lt;/sub&gt;(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26&lt;sup&gt;344&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=344&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;344&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=344&amp;c0=-&amp;EN=&amp;LM=
* the 25200th Athena prime in base 26, 8&lt;sub&gt;354&lt;/sub&gt;1, ''N''−1 is 208×''R''&lt;sub&gt;354&lt;/sub&gt;(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26&lt;sup&gt;354&lt;/sup&gt;−1, and for the algebraic factors of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&amp;Exp=354&amp;LBIDPMList=A&amp;LBIDLODList=D, and for the prime factorization of 26&lt;sup&gt;354&lt;/sup&gt;−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&amp;Exp=354&amp;c0=-&amp;EN=&amp;LM=

All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], &quot;{}&quot; means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 means 123333567 (all subscripts are written in decimal).

Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11}

Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111}

Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221}

Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10&lt;sub&gt;93&lt;/sub&gt;13, and its algebraic form is 5&lt;sup&gt;95&lt;/sup&gt;+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013}

Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041}

Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3&lt;sub&gt;16&lt;/sub&gt;1, and its algebraic form is (7&lt;sup&gt;17&lt;/sup&gt;−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331}

Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4&lt;sub&gt;220&lt;/sub&gt;7, and its algebraic form is (4×8&lt;sup&gt;221&lt;/sup&gt;+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447}

Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30&lt;sub&gt;1158&lt;/sub&gt;11, and its algebraic form is 3×9&lt;sup&gt;1160&lt;/sup&gt;+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011}

Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50&lt;sub&gt;28&lt;/sub&gt;27, and its algebraic form is 5×10&lt;sup&gt;30&lt;/sup&gt;+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57&lt;sub&gt;62668&lt;/sub&gt;), the largest of which has 62669 digits (it is 57&lt;sub&gt;62668&lt;/sub&gt;, and its algebraic form is (57×11&lt;sup&gt;62668&lt;/sup&gt;−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11]

Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40&lt;sub&gt;39&lt;/sub&gt;77, and its algebraic form is 4×12&lt;sup&gt;41&lt;/sup&gt;+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077}

Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5&lt;sub&gt;23755&lt;/sub&gt;C, 80&lt;sub&gt;32017&lt;/sub&gt;111, 95&lt;sub&gt;197420&lt;/sub&gt;, A3&lt;sub&gt;592197&lt;/sub&gt;A), the largest of which has 592199 digits (it is A3&lt;sub&gt;592197&lt;/sub&gt;A, and its algebraic form is (41×13&lt;sup&gt;592198&lt;/sup&gt;+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13]

Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D&lt;sub&gt;19698&lt;/sub&gt;, and its algebraic form is 5×14&lt;sup&gt;19698&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14]

Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7&lt;sub&gt;155&lt;/sub&gt;97, and its algebraic form is (15&lt;sup&gt;157&lt;/sup&gt;+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15]

Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB&lt;sub&gt;32234&lt;/sub&gt;, 4&lt;sub&gt;72785&lt;/sub&gt;DD, 3&lt;sub&gt;116137&lt;/sub&gt;AF), the largest of which has 116139 digits (it is 3&lt;sub&gt;116137&lt;/sub&gt;AF, and its algebraic form is (16&lt;sup&gt;116139&lt;/sup&gt;+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16]

Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17]

Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0&lt;sub&gt;6268&lt;/sub&gt;C5, and its algebraic form is 12×18&lt;sup&gt;6270&lt;/sup&gt;+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18]

Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19]

Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0&lt;sub&gt;6269&lt;/sub&gt;D, and its algebraic form is 16×20&lt;sup&gt;6270&lt;/sup&gt;+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20]

Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21]

Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK&lt;sub&gt;22001&lt;/sub&gt;5), the largest of which has 22003 digits (it is BK&lt;sub&gt;22001&lt;/sub&gt;5, and its algebraic form is (251×22&lt;sup&gt;22002&lt;/sup&gt;−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22]

Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23]

Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N&lt;sub&gt;8129&lt;/sub&gt;LN, and its algebraic form is 13249×24&lt;sup&gt;8131&lt;/sup&gt;−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24]

Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25]

Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5&lt;sub&gt;19391&lt;/sub&gt;6F, 7&lt;sub&gt;20279&lt;/sub&gt;OL, LD0&lt;sub&gt;20975&lt;/sub&gt;7, 6K&lt;sub&gt;23300&lt;/sub&gt;5, J0&lt;sub&gt;44303&lt;/sub&gt;KCB, M0&lt;sub&gt;61186&lt;/sub&gt;2BB, 85M&lt;sub&gt;197060&lt;/sub&gt;B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26]

Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27]

Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6&lt;sub&gt;24051&lt;/sub&gt;LR, 5OA&lt;sub&gt;31238&lt;/sub&gt;F, O4O&lt;sub&gt;94535&lt;/sub&gt;9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28]

Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29]

Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0&lt;sub&gt;24608&lt;/sub&gt;D), the largest of which has 34206 digits (it is OT&lt;sub&gt;34205&lt;/sub&gt;, and its algebraic form is 25×30&lt;sup&gt;34205&lt;/sup&gt;−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30]

Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31]

Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32]

Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33]

Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34]

Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35]

Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K&lt;sub&gt;26567&lt;/sub&gt;Z, S0&lt;sub&gt;75007&lt;/sub&gt;8H, P&lt;sub&gt;81993&lt;/sub&gt;SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36]

== Condensed table for bases 2 ≤ ''b'' ≤ 36 ==

{|class=&quot;wikitable&quot;
||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write &quot;''d''&lt;sub&gt;''n''&lt;/sub&gt;&quot; if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)||
|-
||2||1||11||2||1||3||http://factordb.com/index.php?id=3&amp;open=ecm||http://factordb.com/index.php?showid=3&amp;base=2||0||–||
|-
||3||3||111&lt;br&gt;21&lt;br&gt;12||3&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;1&lt;br&gt;1||13&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=13&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=3&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=3&lt;nowiki/&gt;||0||–||
|-
||4||5||221&lt;br&gt;31&lt;br&gt;23&lt;br&gt;13&lt;br&gt;11||3&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;1&lt;br&gt;1||41&lt;br&gt;13&lt;br&gt;11&lt;br&gt;7&lt;br&gt;5||http://factordb.com/index.php?id=41&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=7&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=5&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=41&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=7&amp;base=4&lt;br&gt;http://factordb.com/index.php?showid=5&amp;base=4&lt;nowiki/&gt;||0||–||
|-
||5||22||10&lt;sub&gt;93&lt;/sub&gt;13&lt;br&gt;300031&lt;br&gt;44441&lt;br&gt;33331&lt;br&gt;33001&lt;br&gt;30301&lt;br&gt;14444&lt;br&gt;10103&lt;br&gt;3101&lt;br&gt;414||96&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4&lt;br&gt;3||67&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;3&lt;br&gt;3&lt;br&gt;3||5&lt;sup&gt;95&lt;/sup&gt;+8&lt;br&gt;9391&lt;br&gt;3121&lt;br&gt;2341&lt;br&gt;2251&lt;br&gt;1951&lt;br&gt;1249&lt;br&gt;653&lt;br&gt;401&lt;br&gt;109||http://factordb.com/index.php?id=1100000000034686071&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9391&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=3121&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2341&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2251&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1951&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1249&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=653&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=401&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=109&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000000034686071&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=9391&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=3121&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2341&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=2251&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1951&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=1249&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=653&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=401&amp;base=5&lt;br&gt;http://factordb.com/index.php?showid=109&amp;base=5&lt;nowiki/&gt;||0||–||
|-
||6||11||40041&lt;br&gt;4441&lt;br&gt;4401&lt;br&gt;51&lt;br&gt;45&lt;br&gt;35&lt;br&gt;31&lt;br&gt;25&lt;br&gt;21&lt;br&gt;15||5&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||4&lt;br&gt;4&lt;br&gt;4&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2&lt;br&gt;2||5209&lt;br&gt;1033&lt;br&gt;1009&lt;br&gt;31&lt;br&gt;29&lt;br&gt;23&lt;br&gt;19&lt;br&gt;17&lt;br&gt;13&lt;br&gt;11||http://factordb.com/index.php?id=5209&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1033&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=1009&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=31&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=29&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=23&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=19&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=17&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=13&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=11&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=5209&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1033&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=1009&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=31&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=29&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=23&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=19&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=17&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=13&amp;base=6&lt;br&gt;http://factordb.com/index.php?showid=11&amp;base=6&lt;nowiki/&gt;||0||–||
|-
||7||71||3&lt;sub&gt;16&lt;/sub&gt;1&lt;br&gt;510&lt;sub&gt;7&lt;/sub&gt;1&lt;br&gt;3&lt;sub&gt;6&lt;/sub&gt;01&lt;br&gt;1100021&lt;br&gt;531101&lt;br&gt;351101&lt;br&gt;300053&lt;br&gt;150001&lt;br&gt;100121&lt;br&gt;40054||17&lt;br&gt;10&lt;br&gt;8&lt;br&gt;7&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;6&lt;br&gt;5||15&lt;br&gt;9&lt;br&gt;7&lt;br&gt;6&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;5&lt;br&gt;4||(7&lt;sup&gt;17&lt;/sup&gt;−5)/2&lt;br&gt;36×7&lt;sup&gt;8&lt;/sup&gt;+1&lt;br&gt;(7&lt;sup&gt;8&lt;/sup&gt;−47)/2&lt;br&gt;134471&lt;br&gt;91631&lt;br&gt;62819&lt;br&gt;50459&lt;br&gt;28813&lt;br&gt;16871&lt;br&gt;9643||http://factordb.com/index.php?id=116315256993601&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=207532837&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=2882377&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=134471&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=91631&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=62819&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=50459&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=28813&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=16871&amp;open=ecm&lt;br&gt;http://factordb.com/index.php?id=9643&amp;open=ecm&lt;nowiki/&gt;||http://factordb.com/index.php?showid=116315256993601&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=207532837&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=2882377&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=134471&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=91631&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=62819&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=50459&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=28813&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=16871&amp;base=7&lt;br&gt;http://factordb.com/index.php?showid=9643&amp;base=7&lt;nowiki/&gt;||0||–||
|-
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||33||280012~280093||DP&lt;sub&gt;95093&lt;/sub&gt;M5&lt;br&gt;HJ0&lt;sub&gt;94295&lt;/sub&gt;J&lt;br&gt;90&lt;sub&gt;93597&lt;/sub&gt;Q&lt;br&gt;9F0&lt;sub&gt;93157&lt;/sub&gt;N&lt;br&gt;7&lt;sub&gt;89449&lt;/sub&gt;333H&lt;br&gt;K3&lt;sub&gt;80751&lt;/sub&gt;6K&lt;br&gt;D&lt;sub&gt;80107&lt;/sub&gt;9UD&lt;br&gt;VFU&lt;sub&gt;72204&lt;/sub&gt;FK&lt;br&gt;J&lt;sub&gt;68715&lt;/sub&gt;2BJ&lt;br&gt;DF0&lt;sub&gt;68367&lt;/sub&gt;J||95096&lt;br&gt;94298&lt;br&gt;93599&lt;br&gt;93160&lt;br&gt;89453&lt;br&gt;80754&lt;br&gt;80110&lt;br&gt;72208&lt;br&gt;68718&lt;br&gt;68370||144405&lt;br&gt;143193&lt;br&gt;142131&lt;br&gt;141465&lt;br&gt;135835&lt;br&gt;122626&lt;br&gt;121648&lt;br&gt;109649&lt;br&gt;104350&lt;br&gt;103821||(441×33&lt;sup&gt;95095&lt;/sup&gt;−3833)/32&lt;br&gt;580×33&lt;sup&gt;94296&lt;/sup&gt;+19&lt;br&gt;9×33&lt;sup&gt;93598&lt;/sup&gt;+26&lt;br&gt;312×33&lt;sup&gt;93158&lt;/sup&gt;+23&lt;br&gt;(7×33&lt;sup&gt;89453&lt;/sup&gt;−4743239)/32&lt;br&gt;(643×33&lt;sup&gt;80753&lt;/sup&gt;+3709)/32&lt;br&gt;(13×33&lt;sup&gt;80110&lt;/sup&gt;−121453)/32&lt;br&gt;(16623×33&lt;sup&gt;72206&lt;/sup&gt;−8095)/16&lt;br&gt;(19×33&lt;sup&gt;68718&lt;/sup&gt;−600883)/32&lt;br&gt;444×33&lt;sup&gt;68368&lt;/sup&gt;+19||http://factordb.com/index.php?id=1100000005652348775&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652362811&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652375073&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652389776&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652430746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652446200&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000005652461592&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614764298&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614770536&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004614784274&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000005652348775&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652362811&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652375073&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652389776&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652430746&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652446200&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000005652461592&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614764298&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614770536&amp;base=33&lt;br&gt;http://factordb.com/index.php?showid=1100000004614784274&amp;base=33&lt;nowiki/&gt;||81||100000||
|-
||34||184785~184832||GFGC&lt;sub&gt;99996&lt;/sub&gt;5&lt;br&gt;90&lt;sub&gt;97950&lt;/sub&gt;FJ&lt;br&gt;NM0&lt;sub&gt;85218&lt;/sub&gt;KX&lt;br&gt;F&lt;sub&gt;83189&lt;/sub&gt;H2HP&lt;br&gt;P&lt;sub&gt;79441&lt;/sub&gt;444P&lt;br&gt;6&lt;sub&gt;77027&lt;/sub&gt;8X&lt;br&gt;XQIQ&lt;sub&gt;72241&lt;/sub&gt;D&lt;br&gt;T&lt;sub&gt;66530&lt;/sub&gt;IF&lt;br&gt;4&lt;sub&gt;66152&lt;/sub&gt;B&lt;br&gt;2EEC&lt;sub&gt;66039&lt;/sub&gt;7||100000&lt;br&gt;97953&lt;br&gt;85222&lt;br&gt;83193&lt;br&gt;79445&lt;br&gt;77029&lt;br&gt;72245&lt;br&gt;66532&lt;br&gt;66153&lt;br&gt;66043||153148&lt;br&gt;150013&lt;br&gt;130516&lt;br&gt;127408&lt;br&gt;121669&lt;br&gt;117968&lt;br&gt;110642&lt;br&gt;101893&lt;br&gt;101312&lt;br&gt;101143||(209246×34&lt;sup&gt;99997&lt;/sup&gt;−81)/11&lt;br&gt;9×34&lt;sup&gt;97952&lt;/sup&gt;+529&lt;br&gt;804×34&lt;sup&gt;85220&lt;/sup&gt;+713&lt;br&gt;(5×34&lt;sup&gt;83193&lt;/sup&gt;+700233)/11&lt;br&gt;(25×34&lt;sup&gt;79445&lt;/sup&gt;−28062367)/33&lt;br&gt;(2×34&lt;sup&gt;77029&lt;/sup&gt;+1043)/11&lt;br&gt;(1288676×34&lt;sup&gt;72242&lt;/sup&gt;−455)/33&lt;br&gt;(29×34&lt;sup&gt;66532&lt;/sup&gt;−12833)/33&lt;br&gt;(4×34&lt;sup&gt;66153&lt;/sup&gt;+227)/33&lt;br&gt;(30826×34&lt;sup&gt;66040&lt;/sup&gt;−59)/11||http://factordb.com/index.php?id=1100000004702891268&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702894713&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702900996&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702910376&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702913746&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004702918600&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399656529&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399657696&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399658651&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004399659716&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000004702891268&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702894713&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702900996&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702910376&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702913746&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004702918600&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399656529&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399657696&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399658651&amp;base=34&lt;br&gt;http://factordb.com/index.php?showid=1100000004399659716&amp;base=34&lt;nowiki/&gt;||47||100000||
|-
||35||720002~720062||N0N&lt;sub&gt;99971&lt;/sub&gt;9&lt;br&gt;V0&lt;sub&gt;83669&lt;/sub&gt;E73&lt;br&gt;N&lt;sub&gt;81563&lt;/sub&gt;K7N&lt;br&gt;BJ0&lt;sub&gt;81279&lt;/sub&gt;N&lt;br&gt;J0&lt;sub&gt;80062&lt;/sub&gt;FUH&lt;br&gt;43V&lt;sub&gt;79754&lt;/sub&gt;&lt;br&gt;9&lt;sub&gt;76600&lt;/sub&gt;K3&lt;br&gt;LB&lt;sub&gt;71366&lt;/sub&gt;PB&lt;br&gt;Q&lt;sub&gt;64150&lt;/sub&gt;H&lt;br&gt;50&lt;sub&gt;63397&lt;/sub&gt;5R||99974&lt;br&gt;83673&lt;br&gt;81566&lt;br&gt;81282&lt;br&gt;80066&lt;br&gt;79756&lt;br&gt;76602&lt;br&gt;71369&lt;br&gt;64151&lt;br&gt;63400||154367&lt;br&gt;129197&lt;br&gt;125944&lt;br&gt;125505&lt;br&gt;123628&lt;br&gt;123148&lt;br&gt;118279&lt;br&gt;110199&lt;br&gt;99054&lt;br&gt;97894||(27393×35&lt;sup&gt;99972&lt;/sup&gt;−499)/34&lt;br&gt;31×35&lt;sup&gt;83672&lt;/sup&gt;+17398&lt;br&gt;(23×35&lt;sup&gt;81566&lt;/sup&gt;−144013)/34&lt;br&gt;404×35&lt;sup&gt;81280&lt;/sup&gt;+23&lt;br&gt;19×35&lt;sup&gt;80065&lt;/sup&gt;+19442&lt;br&gt;(4893×35&lt;sup&gt;79754&lt;/sup&gt;−31)/34&lt;br&gt;(9×35&lt;sup&gt;76602&lt;/sup&gt;+12877)/34&lt;br&gt;(725×35&lt;sup&gt;71368&lt;/sup&gt;+16649)/34&lt;br&gt;(13×35&lt;sup&gt;64151&lt;/sup&gt;−166)/17&lt;br&gt;5×35&lt;sup&gt;63399&lt;/sup&gt;+202||http://factordb.com/index.php?id=1100000008248342445&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248353306&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248375642&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248397018&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248412468&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248418540&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008248423670&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192119974&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192126630&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000008192129294&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000008248342445&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248353306&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248375642&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248397018&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248412468&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248418540&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008248423670&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192119974&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192126630&amp;base=35&lt;br&gt;http://factordb.com/index.php?showid=1100000008192129294&amp;base=35&lt;nowiki/&gt;||60||100000||
|-
||36||35286~35290||P&lt;sub&gt;81993&lt;/sub&gt;SZ&lt;br&gt;S0&lt;sub&gt;75007&lt;/sub&gt;8H&lt;br&gt;7K&lt;sub&gt;26567&lt;/sub&gt;Z&lt;br&gt;J&lt;sub&gt;10117&lt;/sub&gt;LJ&lt;br&gt;VL0&lt;sub&gt;7258&lt;/sub&gt;J&lt;br&gt;EO0&lt;sub&gt;6177&lt;/sub&gt;V&lt;br&gt;FZ&lt;sub&gt;5777&lt;/sub&gt;3P&lt;br&gt;T09&lt;sub&gt;4618&lt;/sub&gt;1&lt;br&gt;RY&lt;sub&gt;4562&lt;/sub&gt;H&lt;br&gt;OZ&lt;sub&gt;3932&lt;/sub&gt;AZ||81995&lt;br&gt;75010&lt;br&gt;26569&lt;br&gt;10119&lt;br&gt;7261&lt;br&gt;6180&lt;br&gt;5780&lt;br&gt;4621&lt;br&gt;4564&lt;br&gt;3935||127609&lt;br&gt;116739&lt;br&gt;41349&lt;br&gt;15748&lt;br&gt;11301&lt;br&gt;9618&lt;br&gt;8996&lt;br&gt;7192&lt;br&gt;7103&lt;br&gt;6124||(5×36&lt;sup&gt;81995&lt;/sup&gt;+821)/7&lt;br&gt;28×36&lt;sup&gt;75009&lt;/sup&gt;+305&lt;br&gt;(53×36&lt;sup&gt;26568&lt;/sup&gt;+101)/7&lt;br&gt;(19×36&lt;sup&gt;10119&lt;/sup&gt;+2501)/35&lt;br&gt;1137×36&lt;sup&gt;7259&lt;/sup&gt;+19&lt;br&gt;528×36&lt;sup&gt;6178&lt;/sup&gt;+31&lt;br&gt;16×36&lt;sup&gt;5779&lt;/sup&gt;−1163&lt;br&gt;(36549×36&lt;sup&gt;4619&lt;/sup&gt;−289)/35&lt;br&gt;(979×36&lt;sup&gt;4563&lt;/sup&gt;−629)/35&lt;br&gt;25×36&lt;sup&gt;3934&lt;/sup&gt;−901||http://factordb.com/index.php?id=1100000002394962083&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000004020085177&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003896952461&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362491&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362489&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362488&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362487&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362486&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000003807362485&amp;open=prime&lt;br&gt;http://factordb.com/index.php?id=1100000000840634476&amp;open=prime&lt;nowiki/&gt;||http://factordb.com/index.php?showid=1100000002394962083&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000004020085177&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003896952461&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362491&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362489&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362488&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362487&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362486&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000003807362485&amp;base=36&lt;br&gt;http://factordb.com/index.php?showid=1100000000840634476&amp;base=36&lt;nowiki/&gt;||4||200000||
|}

== The fully proof of Athena problem in decimal (base ''b'' = 10) ==

'''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''.

Assume ''p'' is a prime &gt; 10, and the last digit of ''p'' must lie in {1,3,7,9}.

Case 1: ''p'' ends with 1.

In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9.

Case 1.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''.

If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''.

Case 1.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8.

If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}.

If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''.

If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite.

Case 1.3: ''p'' begins with 8.

In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5.

If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}.

If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element.

Case 1.4: ''p'' begins with 9.

In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8.

If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8.

If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}.

If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801.

Case 2: ''p'' ends with 3.

In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 3: ''p'' ends with 7.

In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8.

Case 3.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8.

If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}.

If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40&lt;sub&gt;''n''&lt;/sub&gt;1 = 280&lt;sub&gt;''n''&lt;/sub&gt;7.

Case 3.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''.

If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''.

Case 3.3: ''p'' begins with 7.

In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime.

Case 3.4: ''p'' begins with 8.

In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 4: ''p'' ends with 9.

In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9.

If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's.

If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4.

Case 4.1: ''p'' begins with 3.

In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''.

Case 4.2: ''p'' begins with 4.

In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6&lt;sub&gt;''n''&lt;/sub&gt;7 = 46&lt;sub&gt;''n''&lt;/sub&gt;9.

Case 4.3: ''p'' begins with 6.

In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty.

If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6.

If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}.

If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes.

Case 4.4: ''p'' begins with 9.

In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty.

If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669.

[[Category:Number theory]]</text>
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      <text bytes="6871" sha1="1lixhr6gis3lmok2owxksuu1ldx82se" xml:space="preserve">{{In progress}}
==Motivation==
# [[/Citizen science motivation/]] - What motivates participation in citizen science projects? {{ME-By|User Name}}
# [[/Deliberative vs implemental mindset/]] - What are the motivational and cognitive differences between deliberative and implemental mindsets? {{ME-By|User Name}}
# [[/Dopamine and reward prediction/]] - How does dopamine affect the anticipation of rewards and subsequent emotional responses? {{ME-By|User Name}}
# [[/End-of-history illusion and motivation/]] - How does the EOHI influence motivation and what strategies mitigate its impact? {{ME-By|User Name}}
# [[/Fogg behaviour model/]] - How can the FBM be applied to understanding and changing behaviour? {{ME-By|User Name}}
# [[/Functional motives theory and environmental activism/]] - How does functional motives theory explain the motivations behind environmental activism? {{ME-By|User Name}}
# [[/Goal striving dynamics/]] - What is the role of pushing and coasting in goal striving? {{ME-By|User Name}}
# [[/Investment model of commitment and social motivation/]] - How does the investment model of commitment relate to social motivation? {{ME-By|User Name}}
# [[/Metacognitive monitoring and productivity/]] - How does metacognitive monitoring influence goal attainment and productivity? {{ME-By|User Name}}
# [[/Motivating virtual teams/]] - How can motivation in virtual teams be optimised? {{ME-By|User Name}}
# [[/Non-residential energy conservation motivation/]] - How can non-residential building energy conservation be motivated and behaviour changed? {{ME-By|User Name}}
# [[/Parental educational aspirations and student achievement/]] - How do parental aspirations shape children’s academic motivation and performance? {{ME-By|User Name}}
# [[/Protection motivation theory and environmental behaviour/]] - How does protection motivation theory explain engagement in pro-environmental behaviour? {{ME-By|User Name}}
# [[/Role-play and communication skills training/]] - How does role-play facilitate the development of effective communication skills? {{ME-By|User Name}}
# [[/The quiet ego and motivation/]] - How does a quiet ego balance self-interest with concern for others? {{ME-By|User Name}}
# [[/Thermoregulation and motivation/]] - How does the drive to maintain body temperature influence behaviour? {{ME-By|User Name}}
# [[/Tonic-phasic model of dopamine regulation/]] - What is the tonic/phasic model of dopamine regulation and how does it affect behaviour? {{ME-By|User Name}}
# [[/Veteran identity reconstruction and motivation/]] - How does identity reconstruction influence motivation during military-to-civilian transition? {{ME-By|User Name}}
# [[/Windfall gain effect/]] - How does unexpected wealth influence behaviour and decision-making? {{ME-By|User Name}}

==Emotion==
# [[/Biofeedback and emotion regulation/]] - How does biofeedback help individuals monitor and regulate their emotional states? {{ME-By|User Name}}
# [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? {{ME-By|User Name}}
# [[/Emotional role-playing/]] - How does role-playing influence emotional experience, expression, and regulation? {{ME-By|User Name}}
# [[/Emotion detection using artificial intelligence/]] - How can emotion be detected using artificial intelligence? {{ME-By|User Name}}
# [[/Emotion regulation ability and strategy/]] - How do ability and strategy differ in shaping emotion regulation? {{ME-By|User Name}}
# [[/Emotions in activism/]] - How do emotions motivate, shape, and sustain activism? {{ME-By|User Name}}
# [[/Environmental volunteering and wellbeing/]] - How does participation in environmental volunteering influence volunteers' subjective wellbeing? {{ME-By|User Name}}
# [[/Focalism in affective forecasting/]] - What is focalism and how does it bias predictions about future emotional experiences? {{ME-By|User Name}}
# [[/Human trust of robots/]] - What psychological factors shape human trust of robots? {{ME-By|User Name}}
# [[/Identity exploration through role-playing games/]] - How do role-playing games facilitate identity exploration and self-discovery? {{ME-By|User Name}}
# [[/Indigenous Australian funeral practices and grieving/]] - How do Indigenous Australian funeral practices assist with grieving? {{ME-By|User Name}}
# [[/Mindfulness and nature connectedness/]] - How does mindfulness influence nature connectedness? {{ME-By|User Name}}
# [[/Neurofeedback and emotional regulation/]] - How can neurofeedback influence enhance emotional regulation? {{ME-By|User Name}}
# [[/Nitrous oxide and emotion/]] - How does nitrous oxide influence emotional experience and mood? {{ME-By|User Name}}
# [[/Noise and emotion/]] - How do different types of noise affect emotional experience and wellbeing? {{ME-By|User Name}}
# [[/Opponent process theory and emotion/]] - What role do opposing affective states play in emotional experience? {{ME-By|User Name}}
# [[/Perfectionism and athlete mental health/]] - How does perfectionism affect athlete mental health? {{ME-By|User Name}}
# [[/Psychological preparation for natural disasters/]] - How can people psychologically prepare for natural disasters? {{ME-By|User Name}}
# [[/Psychological safety and feedback uptake/]] - How does psychological safety influence openness to feedback? {{ME-By|User Name}}
# [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? {{ME-By|User Name}}
# [[/Remote work and well-being/]] - How does remote work influence employee well-being? {{ME-By|User Name}}
# [[/Spirituality and resilience/]] - What is the relationship between spirituality and psychological resilience? {{ME-By|User Name}}
# [[/Subjective wellbeing homeostasis theory/]] - How does homeostatic theory explain the stability and regulation of subjective wellbeing? {{ME-By|User Name}}
# [[/Theory of positive disintegration and personal growth/]] - What is the TPD and how can it be applied to personal growth? {{ME-By|User Name}}
# [[/Trust in artificial intelligence/]] - What psychological factors shape human trust of artificial intelligence systems? {{ME-By|User Name}}
# [[/Wayfinding and affective experience/]] - How do emotions influence navigation and spatial behaviour? {{ME-By|User Name}}

==Motivation and emotion==
# [[/Reward prediction error/]] - How do reward prediction errors influence learning, emotion, and motivation? {{ME-By|User Name}}
# [[/Social and emotional well-being in Indigenous Australians/]] - How does the holistic social and emotional well-being model reframe Indigenous Australian health and well-being? {{ME-By|User Name}}
# [[/Strengths-based Indigenous Australian psychology/]] - How can strengths-based perspectives enhance understanding of Indigenous motivation and emotion? {{ME-By|User Name}}

[[Category:Motivation and emotion/Book/2027]]</text>
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      <text bytes="16244" sha1="8xp13gbqm0pinnkbf6m4ee5i92mzzj2" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological Effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological Theories ==
Psychological theories around exercise and emotional regulation include the [[w:Self determination theory|Self-Determination Theory]] (SDT) and xxxxxxxxxxxxxx.

=== The Self Determination Theory ===
The Self Determination Theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness. 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  More intrinsic motives also predict better exercise participation. The need to experience a sense of belonging, connection, and care for others. A trend towards identified regulation (exercising because you see value in doing so) was also found to predict participation more strongly than intrinsic motivation in the short term. Although, intrinsic motivation is more predictive of long-term exercise adherence.    

{{RoundBoxTop|theme=3}}'''So how can the Self-Determination Theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion:

* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

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[[Category:Motivation and emotion/Book]]</text>
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      <text bytes="17198" sha1="7v4e8sg7a0priiqpqypjxsg7hsi3qjl" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is Emotion Regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological Effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological Effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological Theories ==
Psychological theories around exercise and emotional regulation include the [[w:Self determination theory|Self-Determination Theory]] (SDT) and xxxxxxxxxxxxxx.

=== The Self Determination Theory ===
The Self Determination Theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  The need to experience a sense of belonging, connection, and care for others. 
Types of motivation from SDT:

* '''Intrinsic Motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic Motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action or non/action.
{{RoundBoxTop|theme=3}}'''So how can the Self-Determination Theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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      <text bytes="17194" sha1="0gctbgcru5p0cjy0vayrl0sxt0ozflj" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Psychological theories around exercise and emotional regulation include the [[w:Self determination theory|self-determination theory]] (SDT) and xxxxxxxxxxxxxx.

=== Self determination theory ===
The self determination theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  The need to experience a sense of belonging, connection, and care for others. 
Types of motivation from SDT:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action or non/action.
{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
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      <text bytes="17673" sha1="jkm4co2s8p1gb3ped7yyo1vjephtxpp" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Psychological theories around exercise and emotional regulation include the [[w:Self determination theory|self-determination theory]] (SDT) and xxxxxxxxxxxxxx.

=== Self determination theory ===
The self determination theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.
Types of motivation from SDT:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action or non/action.
{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Psychological theories around exercise and emotional regulation include the [[w:Self determination theory|self-determination theory]] (SDT) and xxxxxxxxxxxxxx.

=== Self determination theory ===
The self determination theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.
Types of motivation from SDT:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action. Three aspects attribute to feeling amotivative: Low competence, low autonomy, and low relatedness. The amotivated state is a predictor of poor performance and poor functioning.
{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
__TOC__
[[Category:Motivation and emotion/Book]]</text>
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    </revision>
    <revision>
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      <text bytes="19898" sha1="hem8b6xvju7uzf3eu9piokclawbrs7m" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Many psychological theories can be applied to exercise and emotional regulation however here we will cover the [[w:Self determination theory|self-determination theory]] (SDT), [[cognitive evaluation theory]] (CET), [[drive theory]] and xxxxxxx.

=== Self determination theory ===
The self determination theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.

=== Cognitive evaluation theory ===
Cognitive evaluation theory is a sub-theory of self-determination theory that explains how external events influence intrinsic motivation by affecting individual &lt;u&gt;perceived&lt;/u&gt; competence and autonomy. Edward L. Deci and Richard M. Ryan develop CET in 1985, with the focus on the interplay between intrinsic and extrinsic motivation. In short, what drives human motiovation. CET examines how external factors—such as rewards, feedback, deadlines, or social pressures—can either enhance or undermine a person’s natural drive to engage in an activity for its own sake. The theory emphasizes that intrinsic motivation is not fixed but highly sensitive to environmental cues.

In an sports or exercise context, individuals or coaches can use CET principles to encourage skill development and enjoyment rather than relying solely on external rewards such as first place trophies.

Types of motivation from cognitive evaluation theory:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action. Three aspects attribute to feeling amotivative: Low competence, low autonomy, and low relatedness. The amotivated state is a predictor of poor performance and poor functioning.

=== Drive theory ===
The drive theory proposes that humans are motivated to reduces pressures and stress and discomfort. Hull (1943) suggests that as a individuals arousal level increase, performance will also increase. Alternatively, if an individual's arousal levels decrease, then the performance would also decrease. Although this is not a primary motivational theory in the modern time, it still gives a good overview on what modern individuals often do not choose to exercise in time of emotional dysregulation. People are unconsciously looking to preserve energy and reduce stresses in the short term. What makes drive theory a learning theory, not just a motivation theory, is the feedback loop. When a particular behavior successfully reduces a drive, the connection between the situation and that behavior gets stronger. Hull called this “habit strength.” This is another point that is related for modern day people, we need to consciously turn to strengthen healthy habits and weaken maladaptive automatic responses.{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

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      <text bytes="19951" sha1="9k36cjhougrr8g2aijptqqixxp1d0l6" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
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==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Many psychological theories can be applied to exercise and emotional regulation however here we will cover the [[w:Self determination theory|self-determination theory]] (SDT), [[cognitive evaluation theory]] (CET), [[drive theory|drive theory/ Conservation of Resources (COR) Theory]] and xxxxxxx.

=== Self determination theory ===
The self determination theory focus on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.

=== Cognitive evaluation theory ===
Cognitive evaluation theory is a sub-theory of self-determination theory that explains how external events influence intrinsic motivation by affecting individual &lt;u&gt;perceived&lt;/u&gt; competence and autonomy. Edward L. Deci and Richard M. Ryan develop CET in 1985, with the focus on the interplay between intrinsic and extrinsic motivation. In short, what drives human motiovation. CET examines how external factors—such as rewards, feedback, deadlines, or social pressures—can either enhance or undermine a person’s natural drive to engage in an activity for its own sake. The theory emphasizes that intrinsic motivation is not fixed but highly sensitive to environmental cues.

In an sports or exercise context, individuals or coaches can use CET principles to encourage skill development and enjoyment rather than relying solely on external rewards such as first place trophies.

Types of motivation from cognitive evaluation theory:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action. Three aspects attribute to feeling amotivative: Low competence, low autonomy, and low relatedness. The amotivated state is a predictor of poor performance and poor functioning.

=== Drive theory ===
The drive theory proposes that humans are motivated to reduces pressures and stress and discomfort. Hull (1943) suggests that as a individuals arousal level increase, performance will also increase. Alternatively, if an individual's arousal levels decrease, then the performance would also decrease. Although this is not a primary motivational theory in the modern time, it still gives a good overview on what modern individuals often do not choose to exercise in time of emotional dysregulation. People are unconsciously looking to preserve energy and reduce stresses in the short term. What makes drive theory a learning theory, not just a motivation theory, is the feedback loop. When a particular behavior successfully reduces a drive, the connection between the situation and that behavior gets stronger. Hull called this “habit strength.” This is another point that is related for modern day people, we need to consciously turn to strengthen healthy habits and weaken maladaptive automatic responses.{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

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==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Many psychological theories can be applied to exercise and emotional regulation however here we will cover the [[w:Self determination theory|self-determination theory]] (SDT), [[cognitive evaluation theory]] (CET), [[drive theory|drive theory/ Conservation of Resources (COR) Theory]] and xxxxxxx.

=== Process model of emotion regulation (Gross, 19XX) ===
Gross's (19XX) Process model of emotion regulation in one of the most influential frameworks for understanding how emotions arise and how we can regulate them.

=== Self-determination theory (Deci &amp; Ryan, 1985) ===
The self-determination theory focuses on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.

==== Cognitive evaluation theory (Deci &amp; Ryan, 1985) ====
Cognitive evaluation theory is a sub-theory of self-determination theory that explains how external events influence intrinsic motivation by affecting individual &lt;u&gt;perceived&lt;/u&gt; competence and autonomy. Edward L. Deci and Richard M. Ryan develop CET in 1985, with the focus on the interplay between intrinsic and extrinsic motivation. In short, what drives human motiovation. CET examines how external factors—such as rewards, feedback, deadlines, or social pressures—can either enhance or undermine a person’s natural drive to engage in an activity for its own sake. The theory emphasizes that intrinsic motivation is not fixed but highly sensitive to environmental cues.

In an sports or exercise context, individuals or coaches can use CET principles to encourage skill development and enjoyment rather than relying solely on external rewards such as first place trophies.

Types of motivation from cognitive evaluation theory:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action. Three aspects attribute to feeling amotivative: Low competence, low autonomy, and low relatedness. The amotivated state is a predictor of poor performance and poor functioning.

=== Drive theory (Hull, 1943) ===
The drive theory proposes that humans are motivated to reduces pressures and stress and discomfort. Hull (1943) suggests that as a individuals arousal level increase, performance will also increase. Alternatively, if an individual's arousal levels decrease, then the performance would also decrease. Although this is not a primary motivational theory in the modern time, it still gives a good overview on what modern individuals often do not choose to exercise in time of emotional dysregulation. People are unconsciously looking to preserve energy and reduce stresses in the short term. What makes drive theory a learning theory, not just a motivation theory, is the feedback loop. When a particular behavior successfully reduces a drive, the connection between the situation and that behavior gets stronger. Hull called this “habit strength.” This is another point that is related for modern day people, we need to consciously turn to strengthen healthy habits and weaken maladaptive automatic responses.{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

&lt;noinclude&gt;
&lt;hr&gt;
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      <text bytes="20264" sha1="5bpevkvp7qjyuqsgbsf6p9veoi76rwu" xml:space="preserve">{{title|Emotion regulation through exercise:&lt;br&gt;How do people use exercise to regulate their emotional states?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=3}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Many psychological theories can be applied to exercise and emotional regulation however here we will cover the process model of emotion regulation, [[w:Self determination theory|self-determination theory]] (SDT), [[cognitive evaluation theory]] (CET), [[drive theory|drive theory/ Conservation of Resources (COR) Theory]] and xxxxxxx.

=== Process model of emotion regulation (Gross, 19XX) ===
Gross's (19XX) Process model of emotion regulation in one of the most influential frameworks for understanding how emotions arise and how we can regulate them.

=== Self-determination theory (Deci &amp; Ryan, 1985) ===
The self-determination theory focuses on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.

==== Cognitive evaluation theory (Deci &amp; Ryan, 1985) ====
Cognitive evaluation theory is a sub-theory of self-determination theory that explains how external events influence intrinsic motivation by affecting individual &lt;u&gt;perceived&lt;/u&gt; competence and autonomy. Edward L. Deci and Richard M. Ryan develop CET in 1985, with the focus on the interplay between intrinsic and extrinsic motivation. In short, what drives human motiovation. CET examines how external factors—such as rewards, feedback, deadlines, or social pressures—can either enhance or undermine a person’s natural drive to engage in an activity for its own sake. The theory emphasizes that intrinsic motivation is not fixed but highly sensitive to environmental cues.

In an sports or exercise context, individuals or coaches can use CET principles to encourage skill development and enjoyment rather than relying solely on external rewards such as first place trophies.

Types of motivation from cognitive evaluation theory:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action. Three aspects attribute to feeling amotivative: Low competence, low autonomy, and low relatedness. The amotivated state is a predictor of poor performance and poor functioning.

=== Drive theory (Hull, 1943) ===
The drive theory proposes that humans are motivated to reduces pressures and stress and discomfort. Hull (1943) suggests that as a individuals arousal level increase, performance will also increase. Alternatively, if an individual's arousal levels decrease, then the performance would also decrease. Although this is not a primary motivational theory in the modern time, it still gives a good overview on what modern individuals often do not choose to exercise in time of emotional dysregulation. People are unconsciously looking to preserve energy and reduce stresses in the short term. What makes drive theory a learning theory, not just a motivation theory, is the feedback loop. When a particular behavior successfully reduces a drive, the connection between the situation and that behavior gets stronger. Hull called this “habit strength.” This is another point that is related for modern day people, we need to consciously turn to strengthen healthy habits and weaken maladaptive automatic responses.{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

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==Overview==
{{RoundBoxTop|theme=3}}'''Case study'''
[[File:Laptop and girl biting pencil-pixabay.jpg|thumb|200px|'''Figure 1'''. Sarah feeling very unregulated with too much going on in her life.]]

Sarah stayed up late last night studying as she has three assignments due in the same week. When her alarm goes off at 6am for work she feels exhausted so crawls to the shower to wake herself up. Sarahs house mate bangs on the door yelling to hurry up as they need to use the bathroom. Sarah is already sick of this day but gets dressed and rushes off to her part-time work at a before school care center. Her boss grumbles at her for being 10 minutes late and the children are complaining and fighting about the breakfast they served today. Sarah pushes though her shift, and when it's over, she gets back to her car and sits in it for a moment,

She feels tired, grumpy and so frustrated with so many people right now she feels like she might explode. Sarah knows she should go for a run because she hasn't exercised all week, but she is just too tired. Maybe she will get Macca's on the way home and go to her couch to scroll on her phone while she is peacefully at home by herself.

What should Sarah do to help regulate her rising emotions: Go for a run or home to scroll?
{{RoundBoxBottom}}

[[Emotion|Emotions]] are a part of what makes us human and affect us all differently (Izard, 2013). Emotions effect the entirety of a person including their body, perception, cognition, their actions, personality and even their relationships (Izard, 2013). Emotions alert us to sensory information that needs our attention to keep us safe and healthy mentally and physically and steers our actions in these times. Although emotions are very helpful and necessary, they can also have negative impact when they become maladaptive or last too long. This is when we need to regulate our emotions. Emotion regulation is a helpful and important process for humans to function effectively day to day (''Emotion regulation: Conceptual foundations'', 2007). 

[[File:Plutchik-wheel.svg|thumb|'''Figure 2'''. Plutchik's wheel of emotions {{ic|Explain relevance to the topic}}]]

Emotions can be negative or positive to a person and can be triggered by a range of situations in our lives, some we can't control, but some we can.

So what we do to keep our emotions from becoming too much?

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

* What is emotion regulation?
* How can exercise help regulate emotions?
* What exercise is best to help regulate emotions?

{{RoundBoxBottom}}

== What is emotion regulation? ==
[https://www.paulekman.com/universal-emotions/ Universal emotions] were identified by Paul Ekman, that we ''all'' feel, despite we speak different languages, live in different place regional, have different cultural, and ethnic differences (Ekman et al., 1999). He included happiness/enjoyment, anger, fear, disgust, sadness, surprise and then later added contempt. Plutchik went on to create a wheel of emotions to help visually explain these different emotions and show further breakdown (&quot;The emotions,&quot; 1991).

Emotions can also become dysregulated. [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional dysregulation] is when your emotions feel too big and too strong and a person loses the ability to control their behaviour. Emotional dysregulation is the inability to be aware of, accept, regulate, and modify emotional reactions and subsequent behaviours (Gratz &amp; Roemer, 2004). It can look and feel like irritability, anger, mood swings, outbursts, feeling numb or detached, shutting down. Or in more extreme cases aggressive behaviors, stained relationships and connections and verbals shouting and crying&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation|title=Cleveland Clinic: Emotional-dysregulation}}&lt;/ref&gt;.

The goal of emotion regulation is often explained as down-regulating (reducing) the sensation and/or duration of negative emotions such as feeling sad, angry or anxious (Gross et al., 2006). People can also try to up-regulate and increase the intensity or duration of positive emotions (Quoidbach et al., 2010). Emotion regulation is a very important skill of which children typically struggle with and some this can follow into adolescents and adulthood for some.

== How can exercise help to regulate emotions? ==
Exercise is an essential part of humans everyday lives. It's recommended by [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians The Department of Health, Disability and Aging to move most days]. ￼
{{RoundBoxTop|theme=2}}'''Department of Health, Disability and Aging recommended physical activity for adults'''

-Moderate to vigorous physical activities for at least 30 minutes on most days.

-Muscle-strengthening activities at least twice per week.

-Functional activities targeting mobility, balance, and coordination on 3 or more days per week.

-Several hours of light-intensity physical activity daily.
{{RoundBoxBottom}}

=== Physiological effects ===
Exercise positively attributes to well emotional regulation by changing brain chemistry, strengthening brain networks, and reducing stress hormones.

Exercise has been proven to reduce cortisol levels and increase dopamine and other endorphins which are hormones responsible for the feelings of calm and comfort. Simply said, exercise puts the brain in a state where it is better able to regulate emotions! (reference)

* Less cortisol and more dopamine mean emotional regulation is much easier. (reference)
* '''Improve sleep:''' Exercise promotes better sleep as physical exertion regulates stress, lowers stress hormones and reduces muscle tension.

=== Psychological effects ===
Psychological benefits of exercise have continued to be support in many ways such as:

* '''Mindfulness:''' Exercise can give people oppotunities to be present in their movements and have a healthy break from negative of challenging mental strains.
* '''Connection:''' Exercise can be a fantastic way to connect with others and creat social support networks. Walking with friends or family is a perfect way to end a tough day.
* '''Building self-efficacy and self-belief:''' Setting and reaching fitness goals can build personal xonfidence, build resilitience and give you a sense of control over your daily structure. Building self-efficacy and self-esteem through exercise is an important and healthy way to cope with daily challenges.
* '''Improved mental health:''' Exercise has been proven to improve mental health.

== Psychological theories ==
Many psychological theories can be applied to exercise and emotional regulation however here we will cover the process model of emotion regulation, [[w:Self determination theory|self-determination theory]] (SDT), [[cognitive evaluation theory]] (CET), [[drive theory|drive theory/ Conservation of Resources (COR) Theory]] and xxxxxxx.

=== Process model of emotion regulation (Gross, 19XX) ===
Gross's (19XX) Process model of emotion regulation in one of the most influential frameworks for understanding how emotions arise and how we can regulate them.

=== Self-determination theory (Deci &amp; Ryan, 1985) ===
The self-determination theory focuses on fulfilling three core psychological needs, autonomy, competency and relatedness (need reference??). 

The SDT can be applied to exercise thanks to the metadata review by Teixeira et al., 2012. 

# &lt;u&gt;Autonomy:&lt;/u&gt; Studies have consistently supported SDT aspects showing a positive relationship between more autonomous types of motivation and exercise. Autonomous motivation in terms of exercise, means excercising because you ''want'' to, not because you have to. Autonmous motvation towards exercise is a key mindset for consistency to develop. Individuals need to feel in control of their own actions, choices and so should choose their own exercise that suits them personally. The individual should be in charge of implementing structures and routines that work for them.
# &lt;u&gt;Competence:&lt;/u&gt; Competence satisfaction predicts better exercise participation (Teixeira et al., 2012). People are more likely to exercise if they experience competence satisfaction and feel like they are good at what they are doing. Individuals need to feel competent, can master challenging situations and feel as though they are improving and feel able to reach their own goals. This can be applied to fitness goals.
# &lt;u&gt;Relatedness:&lt;/u&gt;  Relatedness is the need to experience a sense of belonging, connection, and care for others. People want to feel accepted, included and a part of a group. Relatedness is the desire to feel connected and interpersonally involved in warm, caring, reciprocal relationships. Exercise is a fantastic way to not just get the physical benefit of moving your body, but also the social and connection of doing so, alongside others with a common health goal. Joining a run club, aqua aerobics or tai chi class can help make social connections whilst moving your body.

==== Cognitive evaluation theory (Deci &amp; Ryan, 1985) ====
Cognitive evaluation theory is a sub-theory of self-determination theory that explains how external events influence intrinsic motivation by affecting individual &lt;u&gt;perceived&lt;/u&gt; competence and autonomy. Edward L. Deci and Richard M. Ryan develop CET in 1985, with the focus on the interplay between intrinsic and extrinsic motivation. In short, what drives human motiovation. CET examines how external factors—such as rewards, feedback, deadlines, or social pressures—can either enhance or undermine a person’s natural drive to engage in an activity for its own sake. The theory emphasizes that intrinsic motivation is not fixed but highly sensitive to environmental cues.

In an sports or exercise context, individuals or coaches can use CET principles to encourage skill development and enjoyment rather than relying solely on external rewards such as first place trophies.

Types of motivation from cognitive evaluation theory:

* '''Intrinsic motivation:''' Doing an activity purely for its satisfaction, enjoyment, or interest predicts better exercise participation of long-term exercise adherence. A trend towards identified regulation (exercising because you see value in doing so) was found to predict participation more strongly than intrinsic motivation in the short term. 

* '''Extrinsic motivation:''' Doing an activity for external rewards, pressures, or avoidance of consequences, which can range from controlled (forced) to autonomous (internalised values). This is a good way to start exercising however intrinsic motives are better for long-term exercise habits. Extrinsic motives include winning a medal, gaining respect and praise or losing weight.

* '''Amotivation:''' Amotivation is complete lack of intent or drive to take action. Three aspects attribute to feeling amotivative: Low competence, low autonomy, and low relatedness. The amotivated state is a predictor of poor performance and poor functioning.

=== Drive theory (Hull, 1943) ===
The drive theory proposes that humans are motivated to reduces pressures and stress and discomfort. Hull (1943) suggests that as a individuals arousal level increase, performance will also increase. Alternatively, if an individual's arousal levels decrease, then the performance would also decrease. Although this is not a primary motivational theory in the modern time, it still gives a good overview on what modern individuals often do not choose to exercise in time of emotional dysregulation. People are unconsciously looking to preserve energy and reduce stresses in the short term. What makes drive theory a learning theory, not just a motivation theory, is the feedback loop. When a particular behavior successfully reduces a drive, the connection between the situation and that behavior gets stronger. Hull called this “habit strength.” This is another point that is related for modern day people, we need to consciously turn to strengthen healthy habits and weaken maladaptive automatic responses.{{RoundBoxTop|theme=3}}'''So how can the self-determination theory be applied to Sarah?'''

Autonomy: Sarah hates running, but she loves dancing. Zumba classes at 7:30pm twice a week might suit Sarah better after she has a quick tea and a rest straight after work.

Competency: Sarah hasn't even done dance classes before, but she does feel confident in showing off her moves. Zumba classes could motivate her to move her body while building more range in her dance move repertoire.

Relatedness: Sarah is a very social person and some of her friends might even like to join the Zumba classes too.
{{RoundBoxBottom}} 

#

== What exercise is best to help regulate emotions? ==
Australian adults should be active daily, undertaking a variety of physical activities at different intensities, which can include&lt;ref&gt;{{Cite web|url=https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians/recommendations-for-adults-18-to-64-years?language=en|title=Physical Activity Recommendations for Australian adults|date=|last=Australian Government}}&lt;/ref&gt;:

* moderate- to vigorous-intensity physical activities for 30 minutes or more on most days
* muscle-strengthening activities on 2 or more days per week
* functional activities targeting mobility, balance, and coordination on 3 or more days per week
* several hours of light-intensity physical activity daily.

Any movement is beneficial to individuals but to regulate your emotions the most ideal exercise looks like this:

Anaerobic exercise (also known as resistance training) has benefits on emotion regulation such as.......

Aerobic exercise&lt;ref&gt;{{Cite web|url=https://my.clevelandclinic.org/health/articles/7050-aerobic-exercise|title=Aerobic Exercise|last=Cleveland Clinic}}&lt;/ref&gt; is when you continuously use oxygen as your fuel. Aerobic exercise promotes emotion regulation (Wang et al., 2024). And what is more important to note is that there are &lt;u&gt;immediate&lt;/u&gt; results on mood.

*

{| class=&quot;wikitable&quot;
|+'''Table 1:''' Optimal exercise for each age category, with supporting studies.
!Age
!Exercise
!Intensity/ Frequency
!Study
|-
|Children
|A variety of exercise such as running, soccer, dancing, tips, games and anything else that sustains interest and fun of the child.

|Moderate–vigorous/ (x hours) Daily
|Salvan et al., 2021
|-
|Adults
|Walking, riding, swimming, running, zumba

Begin with short, low-intensity walking and gradually increase duration and intensity 
|
|Ligeza et al., 2023, 
Mizzi et al., 2022
|-
|Older Adults
|Walking, exercise bike or water aerobics
|Set depending on exercise ability and history
|Erickson et al., 2011
|}
;Test yourself&lt;quiz display=&quot;simple&quot;&gt;
{High intensity running is best for older adults to help manager their emotions:
|type=&quot;()&quot;}
+ True
- False

{Children should take part in more frequent exercise than adults and it should be more varied:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
**

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

==Conclusion==
In conclusion, any physical activity is beneficial in times of emotional dysregulation. Using exercise as a preventative mechanism is also important.

'''Useful takeaways:'''
* One session of aerobic exercise can significantly boost positive mood and alleviate stress responses. It is recommended for use as an immediate mood regulation strategy.
* Any movement can be used such as walking, dancing or sport.

*Recommended length: 150 to 330 words

{{tip|Key messages
* Start by moving your body for 30 minutes in any way you enjoy. Positive effects on mood starts immediately.
What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

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

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

Erickson, K. I., Voss, M. W., Prakash, R. S., Basak, C., Szabo, A., Chaddock, L., Kim, J. S., Heo, S., Alves, H., White, S. M., Wojcicki, T. R., Mailey, E., Vieira, V. J., Martin, S. A., Pence, B. D., Woods, J. A., McAuley, E., &amp; Kramer, A. F. (2011). Exercise training increases size of hippocampus and improves memory. Proceedings of the National Academy of Sciences, 108(7), 3017-3022. https://doi.org/10.1073/pnas.1015950108 

Gratz, K. L., &amp; Roemer, L. (2004). Multidimensional Assessment of Emotion Regulation and Dysregulation: Development, Factor Structure, and Initial Validation of the Difficulties in Emotion Regulation Scale. Journal of Psychopathology and Behavioral Assessment, 26(1), 41-54. https://doi.org/10.1023/B:JOBA.0000007455.08539.94 

Izard, C. E. (2013). Human emotions. Springer Science &amp; Business Media.

Ligeza, T. S., Maciejczyk, M., Wyczesany, M., &amp; Junghofer, M. (2023). The effects of a single aerobic exercise session on mood and neural emotional reactivity in depressed and healthy young adults: A late positive potential study. Psychophysiology, 60(1), e14137. https://doi.org/https://doi.org/10.1111/psyp.14137 

Salvan, P., Wassenaar, T., Wheatley, C., Beale, N., Cottaar, M., Papp, D., Bastiani, M., Fitzgibbon, S., Duff, E., Andersson, J., Winkler, A. M., Douaud, G., Nichols, T. E., Smith, S., Dawes, H., &amp; Johansen-Berg, H. (2021). Multimodal Imaging Brain Markers in Early Adolescence Are Linked with a Physically Active Lifestyle. The Journal of Neuroscience, 41(5), 1092. https://doi.org/10.1523/JNEUROSCI.1260-20.2020 

Teixeira, P. J., Carraça, E. V., Markland, D., Silva, M. N., &amp; Ryan, R. M. (2012). Exercise, physical activity, and self-determination theory: a systematic review. International journal of behavioral nutrition and physical activity, 9(1), 78. 

Wang, X., Liu, T., Jin, X., &amp; Zhou, C. (2024). Aerobic exercise promotes emotion regulation: a narrative review. Experimental Brain Research, 242(4), 783-796. https://doi.org/https://doi.org/10.1007/s00221-024-06791-1

}}

==External links==
External relevant resources:
* [https://www.paulekman.com/universal-emotions/ Universal Emotions | What are Emotions? | Paul Ekman Group]
* [https://my.clevelandclinic.org/health/symptoms/25065-emotional-dysregulation Emotional Dysregulation: What It Is, Causes &amp; Treatment]
* [https://www.health.gov.au/topics/physical-activity/24-hour-movement-guidelines-for-all-australians 24-hour movement guidelines for all Australians | Australian Government Department of Health, Disability and Ageing]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
==See also==
* [[Motivation and emotion/Book/2025/Emotion regulation through exercise|Emotion regulation through exercise]] (Book chapter, 2025)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]
[[Category:Motivation and emotion/Book/Exercise]]

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# Promising [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development (e.g., consider using subheadings)
# Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings)
# Under-developed, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – develop further, perhaps using a 2-level structure for larger section(s) (i.e., including subheadings)
&lt;!-- 3-level --&gt;
# Overly complicated[[Motivation and emotion/Assessment/Major project/Structure|3-level heading structure]] – consider simplifying
&lt;!-- Conceptual --&gt;
# Messy heading structure – needs work (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# The headings lack sufficient incision into, and exposition of, the topic
# Revise heading structure to place less emphasis on background concepts and more emphasis on the target topic (i.e., address the sub-title). The draft headings place too much emphasis on background concepts and too little on the relationship between the concepts.
# Research is not needed as a separate section; instead, integrate and synthesise relevant research throughout the chapter alongside the theoretical perspectives and real-life applications
&lt;!-- Other ---&gt;
# Aim for 3 to 6 top-level headings between the Overview and Conclusion, with 3 to 5 sub-headings for large sections
# Use default heading formatting (i.e., avoid additional formatting such as bold, italics, underline, changing the size etc.)
# Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings
# Check grammar (e.g,. missing question mark)
&lt;!-- Remove --&gt;
# Remove sub-headings in the Overview and/or Conclusion
# Remove &quot;Introduction&quot; heading – provide this information in Overview or move into subsequent sections
# Remove definition(s) headings; cover this in the Overview and/or subsequent sections with embedded inter-wiki link(s) to further information
# Remove case study/scenario headings; instead embed the case study/scenario(s) within relevant section(s)
# Remove quiz headings; instead embed quiz question(s) within relevant section(s)
# Remove numbers from headings
# Remove [[wikt:acronym#Noun|acronym]]s from headings
# Remove citations from headings
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
# Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement
# Good alignment between sub-title, focus questions, and heading structure, but there is room for improvement
# Reasonably good alignment between focus questions and heading structure, but aim for closer alignment
# Basic alignment between between sub-title, focus questions, and top-level headings. Aim to improve.
# Develop closer alignment between sub-title, focus questions, and top-level headings
# Insufficient alignment between sub-title, focus questions, and top-level headings
&lt;!-- GenAI ---&gt;
# Are the headings based on [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
# Very good
# Good
# Reasonably good
# Basic
# Insufficient
# Hasn't been developed – Needs scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- GenAI ---&gt;
# Does this section include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, it needs to be acknowledged as such in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Scenario --&gt;
# An engaging scenario with a relevant image is planned or presented in a feature box at start of the Overview
# A scenario or case study is presented in a feature box with an image at the start of this section
# A scenario or case study is presented in a feature box at the start of this section
# Promising scenario; would benefit from further development to make it more compelling and illustrative
# The scenario is promising, but adapt it to make it more relatable to a wider international audience; university students represent only around 3% of the world's population
# I moved an image into the feature box to help attract reader interest
# Choose an image that illustrates the scenario. Move theoretical diagrams into a subsequent section.
# Add an image to the scenario to help attract reader interest
# Put the scenario or case study into a feature box at the start of this section (fixed)
# Make the scenario concrete and down-to-earth, using a realistic real-world example of the target psychological phenomenon rather than an abstract description.
# Make the relevance of the scenario to the topic more clear. It should be obvious to a reader how the scenario illustrates the topic (i.e., the sub-title question). Revise the scenario to make this connection more explicit.
# Add a scenario or case study in a feature box (with an image) at the start of this section to help engage reader interest
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
# A promising description of the problem/topic is planned or presented
# A basic description of the problem/topic is planned or presented
# What are the most relevant psychological theories?
# Briefly overview the main theoretical perspectives relevant to the topic
# Introduce topic using plain English; most citations can be moved into subsequent setions
# Simplify/abbreviate the description of the problem/topic. Move detail into subsequent sections.
# Add a brief, evocative description of the problem/topic
&lt;!-- Style --&gt;
# Use present, rather than future, tense
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
&lt;!-- Alignment and quality --&gt;
# The focus questions are well aligned with the sub-title and top-level headings
# Reasonably good alignment between focus questions and top-level headings, but consider closer alignment
# Develop closer alignment between the sub-title, focus questions, and top-level headings
# Promising focus questions
# There is no need for a question dedicated to research; instead, integrate covered of research throughout
# There are too many focus questions; only include questions that are needed to address the sub-title; avoid side-quests—these are usually better treated as examples or scenarios, or left out altogether so that the chapter can concentrate on the core task of synthesising the best psychological theory and research about the topic.
&lt;!-- Other --&gt;
# Use open- rather then close-ended focus questions
# Use single- rather than double-barrelled focus questions
# Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Present focus questions in a feature box at the end of this section
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
# Solid development
# Promising development
# Highlight the most relevant theories and synthesise the best research on the topic
# Focus on providing an integrative review of the most relevant theories and research on the topic
# Overly broad/comprehensive; not sufficiently focused/targetted on the topic; this often occurs when genAI content is used by a prompter with insufficient background reading and understanding of the topic and/or insufficient revising and rewriting of genAI content
# Basic development
# Partial development
# Insufficient development
# No development
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is excellent (i.e., not too little/narrow or too big/broad)
# The scope is about right, but it may be that all planned aspects cannot be reasonably covered within the book chapter word count; in that case, be selective and concentrate on key aspects that address the question in the sub-title
# It may be that all planned aspects cannot be reasonably covered within the book chapter word count, so be selective and concentrate on key aspects that address the question in the sub-title
# It is unlikely that all planned aspects can be reasonably covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
# All planned aspects cannot reasonably be covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
# ''Avoid providing too much background information''. Aim to briefly summarise general concepts and provide internal links to relevant book chapters and/or Wikipedia pages for further information. Focus most of the chapter on ''directly answering the core question(s)'' posed by the chapter sub-title.
&lt;!-- Writing style --&gt;
# The writing style is clear and easy to follow
# The writing style is generally clear but could be simplified or made more concise
# The writing style is difficult to follow (e.g., due to vagueness, complex wording, long sentences, long paragraphs, repetition, etc.)
# The writing style is typical of AI-generated material with minimal human oversight. See [[Motivation and emotion/Assessment/Using generative AI|genAI content]] for guidance about ethical and professional practice.
&lt;!-- Theory and research --&gt;
# Good balance of theory and research
# Promising balance of theory and research
# Reasonably good coverage of theory; strive to balance the theoretical content with critical review of relevant research
# Balance theoretical content with critical synthesis of relevant research
# Too much theory. Not enough research. Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples.
# Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples.
# Select the best theories about this topic
# Select the best research about this topic
&lt;!-- Citations --&gt;
# Excellent use of citations
# Very good use of citations
# Good use of citations
# Promising use of citations
# Basic use of citations
# Insufficient use of citations
# Non-peer-reviewed sources should be moved to the &quot;External links&quot; section
# Tip: Rather than starting sentences with an author name and citation, start with the more interesting part (i.e., the substance) and put the citation at the end or mid-way through the sentence
&lt;!-- Citation style --&gt;
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] (e.g., do not include author initials)
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] with three or more authors (i.e., FirstAuthor et al., year)
&lt;!-- Other --&gt;
# For sections with sub-sections, provide key points for an overview paragraph prior to branching into the sub-headings
# Direct quotes need page numbers (APA style) – even better, express the idea in your own words
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# [https://apastyle.apa.org/style-grammar-guidelines/punctuation/serial-comma APA style uses serial commas][[w:Serial comma|1]][https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should 2][https://www.youtube.com/watch?v=gBx8ooDupXY 3] (1 min)
# Use [https://www.aresearchguide.com/write-in-third-person.html 3rd person perspective], although a case study or feature box could use 1st or 2nd person perspective
# Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., analyze → analyse; behavior → behaviour)
# Move references into the References section. Keep citations in the main body.
# Consider using [https://support.studiosity.com/en/articles/489263-writing-feedback-how-it-works Studiosity Writing Feedback+] via UCLearn or a similar writing-support service (e.g., Grammarly) to improve the quality of written expression and check for grammatical and spelling errors in the book chapter draft.
&lt;!-- GenAI ---&gt;
# Well done on acknowledging genAI use in the edit summary. Also share link(s) to the conversation, as per the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]].
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is well developed
# Conclusion is well underway
# Conclusion is underway
# Conclusion is underdeveloped
# Conclusion hasn't been developed
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
# Relevant figure(s) are presented and captioned
# Relevant figure(s) are presented
# The relevance of the figure to the topic is unclear
# A relevant figure is not presented and cited (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Caption --&gt;
# Figure caption(s) provide(s) a clear, appropriately detailed description that is meaningfully connected with the main text
# Figure caption(s) provide(s) a reasonably clear description that is connected with the main text
# Figure caption(s) provide(s) a somewhat clear description that is connected with the main text, but could be improved
# Figure caption(s) could better explain how the image connects to key points being made in the main text
# Figure caption(s) should include '''Figure X'''. [bold] ... (fixed)
&lt;!-- Cite --&gt;
# Figure(s) are cited at least once in the main text
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
&lt;!-- Size --&gt;
# Consider increasing image size(s) (especially if they have text) to make them easier to view
# Consider decreasing image size(s) to make them less dominant
&lt;!-- Creation --&gt;
# Well done on creating and uploading your own image! {{smile}}—this can also be listed on your user page as a social contribution
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Promising in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Two in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# One in-text [[m:Help:Interwiki linking|interwiki link]] for first mention of key term to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Excellent use of scenarios/examples/case studies
# Promising use of scenarios/examples/case studies
# Keep scenarios brief 
# Basic use of scenario/example/case study
# Placeholder use of scenarios/examples/case studies
# Make the relevance of the scenario to the topic more clear
# Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Excellent use of quiz question(s)
# Promising use of quiz question(s)
# Place each quiz question in the most relevant section
# Focus the quiz question(s) on the take-home messages
# Placeholder use of quiz question(s)
# Consider including quiz question(s) about the take-home messages
&lt;!-- Tables --&gt;
# Excellent use of [[Motivation and emotion/Wikiversity/Tables|table(s)]]
# Promising use of [[Motivation and emotion/Wikiversity/Tables|table(s)]]
# Include acknowledgement (e.g., citation(s)) for sources of information presented in the table
# Use APA style for table captions
# Add table caption
# Cite each table at least once in the text
# Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Excellent
# Very good
# Good
# Basic
# Insufficient
# To be developed
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
# At least one relevant systematic review and/or meta-analysis has been identified
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- Move --&gt;
# Move Wikipedia links to the &quot;See also&quot; section
# Move non-academic / non-peer reviewed sources to the &quot;External links&quot; section
&lt;!-- Citations --&gt;
# All references need in-text citation
# All citations need to be in the References
# Only include references which have been accessed and read
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## alphabetical order
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
## [https://apastyle.apa.org/instructional-aids/reference-guide.pdf doi formatting]
## make doi hyperlinks active (i.e., clickable)
## use dois where available instead of other links
## include hyperlinked dois
## page numbers should be separated by an en-dash (–) rather than a hyphen (-)
# A more thorough literature search is recommended. The goal is to identify and use the best academic theory and research about this topic.
# Use APA style or wiki referencing style, but not both (currently, a mixture of referencing styles is used
# Don't cite AI-generated content because it is unreliable and not peer-reviewed. Instead, follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] which include acknowledging and linking to genAI use in edit summaries, otherwise it is a violation of academic integrity.
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
## Very good
## Good
## Basic
## One of two link types provided
### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]]
### Also link to relevant [[w:|Wikipedia]] pages
## Use an internal link style as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link (e.g., (Wikipedia) or (Book chapter, year) for Wikiversity book chapters)
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant Wikiversity book chapters and Wikipedia resources about this topic
&lt;!-- External links --&gt;
# External links
## Excellent
## Very good
## Good
## Basic
## One of two required external links provided
## Move Wikipedia link(s) to the &quot;See also&quot; section
## Move academic sources into the &quot;References&quot; sections and provide in-text citation
## Only include links directly related to the sub-title
## Target an international audience; Australians only represent 0.33% of the world population
## Good choice of links, but poorly formatted (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant external resources about this topic
|9=
&lt;!-- User page --&gt;
# Excellent
# Used effectively
# Very good
# Good
# Basic but effective
# Not created – see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
&lt;!-- Description about self --&gt;
# Excellent description about self provided
# Description about self provided
# Brief description about self – consider expanding
# Very brief description about self – consider expanding
# Add description about self
&lt;!-- Links to profile(s) --&gt;
# Link(s) provided to professional profile(s)
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
# Provide an internal link to the book chapter as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Rename the link to the book chapter to make it more user-friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Add link to book chapter
|10=
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
# Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making:
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
#* posts about the unit or project on the {{Motivation and emotion/Canvas}} discussion forum
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
# Are these contributions based on AI-generated content? If so, please follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]], otherwise it is a violation of academic integrity.
# Well done on creating and uploading your own image!
# Use a numbered list (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Descriptions of contributions could be more precise/accurate/detailed
# Add a brief summary of each contribution
# Remember to sign comments on talk pages
# None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]].
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
# Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed)
# User name removed from the page; for authorship see [[Special:History/{{PAGENAME}}|the page's edit history]]
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Excellent – Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic.
# Clear [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]
# Promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development and/or refinement
# Basic [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development (expand)
&lt;!-- 1-level --&gt;
# Promising [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development (e.g., consider using subheadings)
# Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings)
# Under-developed, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – develop further, perhaps using a 2-level structure for larger section(s) (i.e., including subheadings)
&lt;!-- 3-level --&gt;
# Overly complicated [[Motivation and emotion/Assessment/Major project/Structure|3-level heading structure]] – consider simplifying
&lt;!-- Conceptual --&gt;
# Messy heading structure – needs work (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# The headings lack sufficient incision into, and exposition of, the topic
# Revise heading structure to place less emphasis on background concepts and more emphasis on the target topic (i.e., address the sub-title). The draft headings place too much emphasis on background concepts and too little on the relationship between the concepts.
# Research is not needed as a separate section; instead, integrate and synthesise relevant research throughout the chapter alongside the theoretical perspectives and real-life applications
&lt;!-- Other ---&gt;
# Aim for 3 to 6 top-level headings between the Overview and Conclusion, with 3 to 5 sub-headings for large sections
# Use default heading formatting (i.e., avoid additional formatting such as bold, italics, underline, changing the size etc.)
# Avoid having sections with only 1 sub-heading – use 0 or 2+ sub-headings
# Check grammar (e.g,. missing question mark)
&lt;!-- Remove --&gt;
# Remove sub-headings in the Overview and/or Conclusion
# Remove &quot;Introduction&quot; heading – provide this information in Overview or move into subsequent sections
# Remove definition(s) headings; cover this in the Overview and/or subsequent sections with embedded inter-wiki link(s) to further information
# Remove case study/scenario headings; instead embed the case study/scenario(s) within relevant section(s)
# Remove quiz headings; instead embed quiz question(s) within relevant section(s)
# Remove numbers from headings
# Remove [[wikt:acronym#Noun|acronym]]s from headings
# Remove citations from headings
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
# Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement
# Good alignment between sub-title, focus questions, and heading structure, but there is room for improvement
# Reasonably good alignment between focus questions and heading structure, but aim for closer alignment
# Basic alignment between between sub-title, focus questions, and top-level headings. Aim to improve.
# Develop closer alignment between sub-title, focus questions, and top-level headings
# Insufficient alignment between sub-title, focus questions, and top-level headings
&lt;!-- GenAI ---&gt;
# Are the headings based on [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
# Very good
# Good
# Reasonably good
# Basic
# Insufficient
# Hasn't been developed – Needs scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- GenAI ---&gt;
# Does this section include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, it needs to be acknowledged as such in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Scenario --&gt;
# An engaging scenario with a relevant image is planned or presented in a feature box at start of the Overview
# A scenario or case study is presented in a feature box with an image at the start of this section
# A scenario or case study is presented in a feature box at the start of this section
# Promising scenario; would benefit from further development to make it more compelling and illustrative
# The scenario is promising, but adapt it to make it more relatable to a wider international audience; university students represent only around 3% of the world's population
# I moved an image into the feature box to help attract reader interest
# Choose an image that illustrates the scenario. Move theoretical diagrams into a subsequent section.
# Add an image to the scenario to help attract reader interest
# Put the scenario or case study into a feature box at the start of this section (fixed)
# Make the scenario concrete and down-to-earth, using a realistic real-world example of the target psychological phenomenon rather than an abstract description.
# Make the relevance of the scenario to the topic more clear. It should be obvious to a reader how the scenario illustrates the topic (i.e., the sub-title question). Revise the scenario to make this connection more explicit.
# Add a scenario or case study in a feature box (with an image) at the start of this section to help engage reader interest
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
# A promising description of the problem/topic is planned or presented
# A basic description of the problem/topic is planned or presented
# What are the most relevant psychological theories?
# Briefly overview the main theoretical perspectives relevant to the topic
# Introduce topic using plain English; most citations can be moved into subsequent setions
# Simplify/abbreviate the description of the problem/topic. Move detail into subsequent sections.
# Add a brief, evocative description of the problem/topic
&lt;!-- Style --&gt;
# Use present, rather than future, tense
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
&lt;!-- Alignment and quality --&gt;
# The focus questions are well aligned with the sub-title and top-level headings
# Reasonably good alignment between focus questions and top-level headings, but consider closer alignment
# Develop closer alignment between the sub-title, focus questions, and top-level headings
# Promising focus questions
# There is no need for a question dedicated to research; instead, integrate covered of research throughout
# There are too many focus questions; only include questions that are needed to address the sub-title; avoid side-quests—these are usually better treated as examples or scenarios, or left out altogether so that the chapter can concentrate on the core task of synthesising the best psychological theory and research about the topic.
&lt;!-- Other --&gt;
# Use open- rather then close-ended focus questions
# Use single- rather than double-barrelled focus questions
# Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Present focus questions in a feature box at the end of this section
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
# Solid development
# Promising development
# Highlight the most relevant theories and synthesise the best research on the topic
# Focus on providing an integrative review of the most relevant theories and research on the topic
# Overly broad/comprehensive; not sufficiently focused/targetted on the topic; this often occurs when genAI content is used by a prompter with insufficient background reading and understanding of the topic and/or insufficient revising and rewriting of genAI content
# Basic development
# Partial development
# Insufficient development
# No development
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is excellent (i.e., not too little/narrow or too big/broad)
# The scope is about right, but it may be that all planned aspects cannot be reasonably covered within the book chapter word count; in that case, be selective and concentrate on key aspects that address the question in the sub-title
# It may be that all planned aspects cannot be reasonably covered within the book chapter word count, so be selective and concentrate on key aspects that address the question in the sub-title
# It is unlikely that all planned aspects can be reasonably covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
# All planned aspects cannot reasonably be covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
# ''Avoid providing too much background information''. Aim to briefly summarise general concepts and provide internal links to relevant book chapters and/or Wikipedia pages for further information. Focus most of the chapter on ''directly answering the core question(s)'' posed by the chapter sub-title.
&lt;!-- Writing style --&gt;
# The writing style is clear and easy to follow
# The writing style is generally clear but could be simplified or made more concise
# The writing style is difficult to follow (e.g., due to vagueness, complex wording, long sentences, long paragraphs, repetition, etc.)
# The writing style is typical of AI-generated material with minimal human oversight. See [[Motivation and emotion/Assessment/Using generative AI|genAI content]] for guidance about ethical and professional practice.
&lt;!-- Theory and research --&gt;
# Good balance of theory and research
# Promising balance of theory and research
# Reasonably good coverage of theory; strive to balance the theoretical content with critical review of relevant research
# Balance theoretical content with critical synthesis of relevant research
# Too much theory. Not enough research. Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples. 
# Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples. 
# Select the best theories about this topic
# Select the best research about this topic
&lt;!-- Citations --&gt;
# Excellent use of citations
# Very good use of citations
# Good use of citations
# Promising use of citations
# Basic use of citations
# Insufficient use of citations
# Non-peer-reviewed sources should be moved to the &quot;External links&quot; section
# Tip: Rather than starting sentences with an author name and citation, start with the more interesting part (i.e., the substance) and put the citation at the end or mid-way through the sentence
&lt;!-- Citation style --&gt;
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] (e.g., do not include author initials)
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] with three or more authors (i.e., FirstAuthor et al., year)
&lt;!-- Other --&gt;
# For sections with sub-sections, provide key points for an overview paragraph prior to branching into the sub-headings
# Direct quotes need page numbers (APA style) – even better, express the idea in your own words
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# [https://apastyle.apa.org/style-grammar-guidelines/punctuation/serial-comma APA style uses serial commas][[w:Serial comma|1]][https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should 2][https://www.youtube.com/watch?v=gBx8ooDupXY 3] (1 min)
# Use [https://www.aresearchguide.com/write-in-third-person.html 3rd person perspective], although a case study or feature box could use 1st or 2nd person perspective
# Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., analyze → analyse; behavior → behaviour)
# Move references into the References section. Keep citations in the main body.
# Consider using [https://support.studiosity.com/en/articles/489263-writing-feedback-how-it-works Studiosity Writing Feedback+] via UCLearn or a similar writing-support service (e.g., Grammarly) to improve the quality of written expression and check for grammatical and spelling errors in the book chapter draft.
&lt;!-- GenAI ---&gt;
# Well done on acknowledging genAI use in the edit summary. Also share link(s) to the conversation, as per the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]].
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is well developed
# Conclusion is well underway
# Conclusion is underway
# Conclusion is underdeveloped
# Conclusion hasn't been developed
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
# Relevant figure(s) are presented and captioned
# Relevant figure(s) are presented
# The relevance of the figure to the topic is unclear
# A relevant figure is not presented and cited (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Caption --&gt;
# Figure caption(s) provide(s) a clear, appropriately detailed description that is meaningfully connected with the main text
# Figure caption(s) provide(s) a reasonably clear description that is connected with the main text
# Figure caption(s) provide(s) a somewhat clear description that is connected with the main text, but could be improved
# Figure caption(s) could better explain how the image connects to key points being made in the main text
# Figure caption(s) should include '''Figure X'''. [bold] ... (fixed)
&lt;!-- Cite --&gt;
# Figure(s) are cited at least once in the main text
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
&lt;!-- Size --&gt;
# Consider increasing image size(s) (especially if they have text) to make them easier to view
# Consider decreasing image size(s) to make them less dominant
&lt;!-- Creation --&gt;
# Well done on creating and uploading your own image! {{smile}}—this can also be listed on your user page as a social contribution
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Promising in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
# Two in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# One in-text [[m:Help:Interwiki linking|interwiki link]] for first mention of key term to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Excellent use of scenarios/examples/case studies
# Promising use of scenarios/examples/case studies
# Keep scenarios brief 
# Basic use of scenario/example/case study
# Placeholder use of scenarios/examples/case studies
Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Excellent use of quiz question(s)
# Promising use of quiz question(s)
# Place each quiz question in the most relevant section
# Focus the quiz question(s) on the take-home messages
# Placeholder use of quiz question(s)
# Consider including quiz question(s) about the take-home messages
&lt;!-- Tables --&gt;
# Excellent use of [[Motivation and emotion/Wikiversity/Tables|table(s)]]
# Promising use of [[Motivation and emotion/Wikiversity/Tables|table(s)]]
# Include acknowledgement (e.g., citation(s)) for sources of information presented in the table
# Use APA style for table captions
# Add table caption
# Cite each table at least once in the text
# Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Excellent
# Very good
# Good
# Basic
# Insufficient
# To be developed
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
# At least one relevant systematic review and/or meta-analysis has been identified
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- Move --&gt;
# Move Wikipedia links to the &quot;See also&quot; section
# Move non-academic / non-peer reviewed sources to the &quot;External links&quot; section
&lt;!-- Citations --&gt;
# All references need in-text citation
# All citations need to be in the References
# Only include references which have been accessed and read
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## alphabetical order
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
## [https://apastyle.apa.org/instructional-aids/reference-guide.pdf doi formatting]
## make doi hyperlinks active (i.e., clickable)
## use dois where available instead of other links
## include hyperlinked dois
## page numbers should be separated by an en-dash (–) rather than a hyphen (-)
# A more thorough literature search is recommended. The goal is to identify and use the best academic theory and research about this topic.
# Use APA style or wiki referencing style, but not both (currently, a mixture of referencing styles is used
# Don't cite AI-generated content because it is unreliable and not peer-reviewed. Instead, follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]] which include acknowledging and linking to genAI use in edit summaries, otherwise it is a violation of academic integrity.
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
## Very good
## Good
## Basic
## One of two link types provided
### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]]
### Also link to relevant [[w:|Wikipedia]] pages
## Use an internal link style as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link (e.g., (Wikipedia) or (Book chapter, year) for Wikiversity book chapters)
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant Wikiversity book chapters and Wikipedia resources about this topic
&lt;!-- External links --&gt;
# External links
## Excellent
## Very good
## Good
## Basic
## One of two required external links provided
## Move Wikipedia link(s) to the &quot;See also&quot; section
## Move academic sources into the &quot;References&quot; sections and provide in-text citation
## Only include links directly related to the sub-title
## Target an international audience; Australians only represent 0.33% of the world population
## Good choice of links, but poorly formatted (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Use [[w:Letter case#Sentence casing|sentence casing]]
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link
## Use alphabetical order
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant external resources about this topic
|9=
&lt;!-- User page --&gt;
# Excellent
# Used effectively
# Very good
# Good
# Basic but effective
# Not created – see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
&lt;!-- Description about self --&gt;
# Excellent description about self provided
# Description about self provided
# Brief description about self – consider expanding
# Very brief description about self – consider expanding
# Add description about self
&lt;!-- Links to profile(s) --&gt;
# Link(s) provided to professional profile(s)
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
# Provide an internal link to the book chapter as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Rename the link to the book chapter to make it more user-friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Add link to book chapter
|10=
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
# Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making:
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
#* posts about the unit or project on the {{Motivation and emotion/Canvas}} discussion forum
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
# Are these contributions based on AI-generated content? If so, please follow the [[Motivation and emotion/Assessment/Using generative AI|using genAI guidelines]], otherwise it is a violation of academic integrity.
# Well done on creating and uploading your own image!
# Use a numbered list (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
# Descriptions of contributions could be more precise/accurate/detailed
# Add a brief summary of each contribution
# Remember to sign comments on talk pages
# None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]].
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:58, 26 August 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Topic|Topic development guidelines]]
* [[Template:MEBF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Topic]]
&lt;/noinclude&gt;</text>
      <sha1>gpsgej2ct3f0emkr4ytd7wmc7pzcxcl</sha1>
    </revision>
  </page>
  <page>
    <title>Module:Sandbox/22</title>
    <ns>828</ns>
    <id>331015</id>
    <revision>
      <id>2833650</id>
      <parentid>2833544</parentid>
      <timestamp>2026-09-18T00:14:04Z</timestamp>
      <contributor>
        <username>Helpme2222</username>
        <id>3106525</id>
      </contributor>
      <origin>2833650</origin>
      <model>Scribunto</model>
      <format>text/plain</format>
      <text bytes="8274" sha1="rh4m3aipstoiaovy5cz95bal1z73rqe" xml:space="preserve">-- My function for teaching grammar

local p = {};
local frame = mw.getCurrentFrame()
local grammatical_moods = {
	&quot;Jelen ido&quot;,
	&quot;Mult ido&quot;,
	&quot;Felszolito mod&quot;,
	&quot;Felteteles mod&quot;
}
local balls = {
	grammatical_moods
}

function p.infoboxWBB()
	-- Passing expressions of conditional value: https://www.lua.org/pil/3.3.html
	--[[ https://www.mediawiki.org/wiki/LUAREF#mw.html:node 
			Thankfully, these operations except passed nils as no-ops 
			(I'm technically using false though. Somehow that works anyways?)]]
	local frame = mw.getCurrentFrame()
	local pagename = mw.title.getCurrentTitle()
	local isSuper = -- do blank args count the same as nonexistent ones? check
		frame.args[&quot;SUPER Debuted&quot;] or
		frame.args[&quot;SUPER Starting value&quot;] or 
		frame.args[&quot;SUPER Starting value 1&quot;] or
		frame.args[&quot;SUPER Scaling&quot;] or 
		frame.args[&quot;SUPER Feature&quot;] or 
		frame.args[&quot;SUPER Type&quot;] or 
		(pagecount &gt; 0)
	local table = mw.html.create( 'table' )
		:node( mw.html.create( 'tr' )
			:node( mw.html.create( 'th' )
				:attr({
					colspan = &quot;2&quot;, 
					id = &quot;mw-customcollapsible-Infobox&quot; })
				:addClass((isSuper) and &quot;mw-collapsible&quot;)
				:node(&quot;&lt;big&gt;&quot; .. frame.args[&quot;Title&quot;] or pagename .. &quot;&lt;/big&gt;&quot;)
			)
		)
		:node((isSuper) and mw.html.create( 'tr' )
			:node( mw.html.create( 'th' )
				:attr({
					colspan = &quot;2&quot;, 
					id = &quot;mw-customcollapsible-Infobox&quot; })
				:addClass(&quot;mw-collapsible mw-collapsed&quot;)
				:node(&quot;&lt;big&gt;&quot; .. frame.args[&quot;SUPER Title&quot;] or (&quot;Super&quot; .. (frame.args[&quot;Title&quot;] or pagename)) .. &quot;&lt;/big&gt;&quot;)
			)
		)
		:node( mw.html.create( 'tr' )
			:node( mw.html.create( 'th' )
				:attr({
					colspan = &quot;2&quot;, 
					id = &quot;mw-customcollapsible-Infobox&quot; })
				:addClass((isSuper) and &quot;mw-collapsible&quot;)
				:node(&quot;Basic Info&quot;)
				:node((isSuper) and mw.html.create( 'span' )
					:css({
						float = &quot;right&quot;,
						[&quot;margin-right&quot;] = &quot;0&quot;,
						[&quot;font-weight&quot;] = &quot;normal&quot;
					})
					:addClass(&quot;mw-customtoggle-Infobox&quot;)
					:node(&quot;[Click to toggle]&quot;)
				)
			)
		)
	return tostring(table)
end

function p.title()
	local grammatical_cases = {
		ablative = 1,
		inessive = {
			ANCOVA = &quot;ANCOVA&quot;
		}
	}
	local cases2 = &quot;ba&quot;
	local cases3 = &quot;ba&quot;
	-- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = &quot;true&quot; else cases2 = &quot;false&quot; end
	-- if &quot;ANCOVA&quot; == frame:getParent():getTitle() then cases3 = &quot;true&quot; else cases3 = &quot;false&quot; end
	local detected = false
	detected = detected or true
	return mw.title.getCurrentTitle() 
end

function p.ifexist()
	return tonumber(frame:expandTemplate{ title = &quot;User:Helpme2222/Sandbox&quot;, args = {frame.args[1]} })
end

function p.performance()
	for i = 1,5000000 do p.tableMake() end
	return
end

function p.performance1()
	local var = &quot;&quot;
	for i = 1,100000000 do if var[1] then end end
	return
end

function p.performance2()
	local var = &quot;&quot;
	for i = 1,100000000 do if type(var) == &quot;table&quot; then end end
	return
end

p.counter = 0
function p.tableBake()
	p.counter = p.counter + 1
	return p.counter
end


function p.tableMake()
	p.counter = 0
	local var = {
		keyword = {p.tableBake()},
		kljuczslovo = {p.tableBake()},
		yaoshiwenzi = {p.tableBake()},
		llavepalabra = {p.tableBake()},
	}
	return var
end

function p.expand()
	return frame:expandTemplate{ title = &quot;User:Helpme2222/Sandbox&quot; }
end

function p.title3()
	return mw.title.getCurrentTitle().fullText
end

function p.getBallAttribute()
	local _, ballData = pcall( p.getBallAttributeInternal )
	if _ then return ballData
	else return &quot;&quot; end
end

function p.getBallAttributeInternal()
	local ballData = mw.loadData(frame.args[1])[frame.args[2]][frame.args[3]]
	if ballData[1] then
		return ballData[tonumber(frame.args[4]) or p.listCountInternal(ballData)]
	end
	return ballData
end

function p.emojiCodepoint()
	local emoji = mw.text.trim( mw.getCurrentFrame().args[1] )
	local i,v = mw.ustring.codepoint( emoji, 1, mw.ustring.len(emoji)  )
	if v then return &quot;U+&quot; .. string.format(&quot;%X&quot;, i ) .. &quot; U+&quot; .. string.format(&quot;%X&quot;, v )
	else return &quot;U+&quot; .. string.format(&quot;%X&quot;, i ) end
end

function p.title2()
	local grammatical_cases = {
		ablative = 1,
		inessive = {
			ANCOVA = &quot;ANCOVA&quot;,
			[&quot;Module:Sandbox/22&quot;] = &quot;Module:Sandbox/22&quot;
		}
	}
	
	local concepts = {
		grammatical_cases,
	}
	local PAGENAME = tostring(mw.title.getCurrentTitle())
	local detected = false
	local out = {}
	local debugger = {}
	for i, group in ipairs(concepts) do 
		if group.inessive[PAGENAME] then 
			table.insert(debugger,&quot;Okay, managed TRUE on &quot;..i..&quot;:&quot;..group.ablative)
			detected = detected or true
			local formattedGroup = {}
			for memberKey, memberRendervalue in pairs(group.inessive) do
				table.insert(formattedGroup, &quot;&lt;li&gt;&quot; .. memberRendervalue .. &quot;&lt;/li&gt;&quot;)
			end 
			table.insert(out, &quot;&lt;h3&gt;&quot; .. group.ablative .. &quot;&lt;/h3&gt;&lt;ul&gt;&quot; .. table.concat( formattedGroup ) .. &quot;&lt;/ul&gt;&quot; )
			table.insert(out, &quot;this sucks ass&quot;)
			return &quot;this sucks ass&quot;
		else
			table.insert(debugger,&quot;Managed FALSE on &quot;..i..&quot;:&quot;..group.ablative..&quot;. Comparator: &quot;..PAGENAME..&quot;, &quot;)
		end
	end
	return debugger
	--[[
	if detected then return tostring(detected) .. table.concat(out) end
	return
	--]]
end

function p.sanitizeChar(capture)
	-- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited
	if capture == &quot;?&quot; then
		return &quot;&quot;
	elseif capture == &quot;#&quot; then
		return &quot;No. &quot;
	end
end

function p.sanitizeTitle()
	local title = frame.args[1]
	return mw.ustring.gsub( title, &quot;(?:\\?|\\#)&quot;, p.sanitizeChar) 
end

function p.sanitizeTitletest2()
	return mw.ustring.gsub( &quot;Ki vagy?  (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)&quot;, &quot;(?:\\?|\\#)&quot;, p.sanitizeChar()) 
end

function p.safetyTest()
	if string.len(frame.args[1]) &lt; 500 then 
		return frame.args[1] 
	else 
		return &quot;&quot;
	end
end

--[[ 
function array_iter(t)
 	local i = 0
	return function ()
		i = i + 1
		return t[i] 
	end 
end
--]]

function p.listInline()
	--[[ This function is a godsend! 
	https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]]
	local spritedTable = {}
    for i,entry in ipairs(balls[tonumber(frame.args[1])]) do
	    spritedTable[i] = &quot;{{Sprite|named=1|linked=1|&quot;..entry..&quot;}}&quot;
    end
	return mw.text.listToText( spritedTable , &quot;, &quot;, &quot;, and &quot; )
end

function p.listNavbox()
	-- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat
	local spritedTable = {}
    for i,entry in ipairs(balls[tonumber(frame.args[1])]) do
	    spritedTable[i] = &quot;{{Sprite|named=1|linked=1|&quot;..entry..&quot;}}&quot;
    end
	return table.concat( spritedTable , &quot; • &quot;)
end

function p.listCountInternal(table) 
	local count = 0
	for index,value in ipairs( table ) do count = count + 1 end
	return count
end

function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end
	-- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn

function p.tableTest()
	return balls[1][1]
end

function p.todaysBall()
	--[[ https://www.lua.org/pil/3.6.html
		 The use of explicit indexing here is not strictly semantic;
		 it's just to emphasize the rotation order.
	 ]]
	local unixDay = math.floor(os.time()/86400)
	local ballTotalCount = 0
	local ballCounts = {}
    for whichTable,subtable in ipairs(balls) do 
		ballCounts[whichTable] = #subtable
		ballTotalCount = ballTotalCount + ballCounts[whichTable]
	end
	local cycleDayIndex,  cycleStartingBall = unixDay % ballTotalCount,  math.floor(unixDay/ballTotalCount) % ballTotalCount
	local cycleTodaysBall
	if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount
	elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount
	elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount
	else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end
	--[[ debug
	return cycleTodaysBall .. &quot; &quot; .. ballTotalCount .. &quot; &quot; .. os.time() .. &quot; &quot; .. math.floor(os.time()/86400) .. &quot; &quot; .. cycleDayIndex .. &quot; &quot; .. cycleStartingBall
	]]
	for whichTable = 1, #balls do 
		if ballCounts[whichTable] &gt; cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] 
		else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end
	end 
	--]]
end

return p;</text>
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  </page>
  <page>
    <title>Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment</title>
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      <contributor>
        <username>StretchBeyond</username>
        <id>3105744</id>
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      <text bytes="34736" sha1="qe3v9304t3cf73di55d8lwfyh1ehgmk" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies being used to treat post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy, alongside moves through his 3MDR treatment.

Learn about more about immersive therapy and Andriy’s* experience in the chapter below (*Andriy is a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The 2024 World Health Organisation estimates that 3.9% of the world's population has had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017).This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyper arousal (Efremov, 2025; de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR aim to break this avoidance cycle by creating controlled environments in which trauma and cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hyper-vigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016).

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation.'''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue triggering extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) link this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017).

A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses generated via immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinately. (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, as emotional regulation has dynamic capacity and can improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaption for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy, towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment and its interaction with the human brain. Designed to give readers a simple understanding of emerging technologies used in immersive PTSD environments.]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]](XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications VRET where therapists reconstruct traumatic scenarios in safe, graded environments; and 3MDR, which extends this by having the patient move on a treadmill towards a panoramic display, side-by-side with their therapist, rather than a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (Boska et al., 2025; de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, this benefit does not seem to be driven by exercise physiology which suggests extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF); but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion. This suggests the mechanism is primarily psychological and behavioural. It is the approach action itself and the cognitive restructuring it enables, rather than physiological (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a profound prediction error between the anticipated, life-threatening event and the actual reality. This destabilises the traumatic memory, allowing memory reconsolidation (Felemban et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe, immersive contexts can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which taxes limited working memory resources and reduces the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guiltshifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing potential barriers is important for any PTSD population, but especially critical for military populations, as they show some of the highest treatment failure and drop out rates. van Gelderen et al. (2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). Bypassing imagination challenges such as emotional numbing or amnesia that can prevent patients engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates, substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (de Haart et al., 2026; Lewis et al., 2020; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found immersive treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017). 

'''Table 1:''' Treatment Effects and Psychological Mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional Exposure'''
| valign=&quot;top&quot; |'''Immersive Approach'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Therapeutic Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''
'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing''' '''and attention'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
High dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy* a volunteer in the Ukrainian Armed Forces is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind stays in a constant state of combat readiness, even in a quiet room.

In the pre-platform phase of 3MDR, Andriy worked to identify a ‘hotspot’ memory in a photograph. On the treadmill, harnessed and walking beside his therapist, he faces a panoramic screen as personalised warm-up music plays, selected to keep him in touch with his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy, moves through his 3MDR treatment.

By the end of the session, Andriy has walked towards what he used to avoid, creating a mismatch between his expectation of threat and his safety, turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans who participated in a 2023 randomised controlled trial. Many were demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which was indirect rather than direct clinical cost (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024).

Market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecast to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and supports a paradigm shift, from a narrow, disease model towards one that values post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to resolve (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high, non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism, it is the psychological processes that drive change.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
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[[Category:Motivation and emotion/Book/Trauma]]</text>
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      <text bytes="35833" sha1="geso3748s90ijsdfjoy3193f2eltyo5" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy, moves through his 3MDR treatment.

Learn about more about immersive therapy and Andriy’s* experience in the chapter below (*Andriy is a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The 2024 World Health Organisation estimates that 3.9% of the world's population has had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017).This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyper arousal (Efremov, 2025; de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hyper-vigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation.'''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue triggering extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) link this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses generated via immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinitely (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, as although emotional regulation contributes substantially to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one that is able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy, towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment and its interaction with the human brain. Designed to give readers a simple understanding of emerging technologies used in immersive PTSD environments.]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]](XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their clinical therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action itself and the cognitive restructuring it enables may be the more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and the actual reality. This may destabilise aspects of the traumatic memory, potentially creating conditions under which memory reconsolidation can occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe, immersive contexts can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which taxes limited working memory resources and reduces the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guiltshifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations, who show some of the highest treatment failure and dropout rates van Gelderen et al. (2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). Bypassing imagination challenges such as emotional numbing or amnesia that can prevent patients engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the relatively recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment Effects and Psychological Mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional Exposure'''
| valign=&quot;top&quot; |'''Immersive Approach'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Therapeutic Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''
'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing''' '''and attention'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
High dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy* a volunteer in the Ukrainian Armed Forces is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind stays in a constant state of combat readiness, even in a quiet room.

In the pre-platform phase of 3MDR, Andriy worked to identify a ‘hotspot’ memory in a photograph. On the treadmill, harnessed and walking beside his therapist, he faces a panoramic screen as personalised warm-up music plays, selected to keep him in touch with his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy moves through his 3MDR treatment.

By the end of the session, Andriy has walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans who participated in a 2023 randomised controlled trial. Many were demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which was indirect rather than direct clinical cost (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials also rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecast to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and supports a paradigm shift, from a narrow, disease model towards one that values post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to resolve (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high, non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisims that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
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[[Category:Motivation and emotion/Book/Trauma]]</text>
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      <text bytes="35832" sha1="i5mx2d0r8kstexxw0pyjy0sh7e7euka" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy, moves through his 3MDR treatment.

Learn about more about immersive therapy and Andriy’s* experience in the chapter below (*Andriy is a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The 2024 World Health Organisation estimates that 3.9% of the world's population has had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017).This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyper arousal (Efremov, 2025; de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hyper-vigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation.'''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue triggering extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) link this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses generated via immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinitely (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, as although emotional regulation contributes substantially to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one that is able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy, towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment and its interaction with the human brain. Designed to give readers a simple understanding of emerging technologies used in immersive PTSD environments.]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]](XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their clinical therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action itself and the cognitive restructuring it enables may be the more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and the actual reality. This may destabilise aspects of the traumatic memory, potentially creating conditions under which memory reconsolidation can occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe, immersive contexts can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which taxes limited working memory resources and reduces the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guiltshifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations, who show some of the highest treatment failure and dropout rates van Gelderen et al. (2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). Bypassing imagination challenges such as emotional numbing or amnesia that can prevent patients engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the relatively recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment Effects and Psychological Mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional Exposure'''
| valign=&quot;top&quot; |'''Immersive Approach'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Therapeutic Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''
'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing''' '''and attention'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
High dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy* a volunteer in the Ukrainian Armed Forces is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind stays in a constant state of combat readiness, even in a quiet room.

In the pre-platform phase of 3MDR, Andriy worked to identify a ‘hotspot’ memory in a photograph. On the treadmill, harnessed and walking beside his therapist, he faces a panoramic screen as personalised warm-up music plays, selected to keep him in touch with his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy moves through his 3MDR treatment.

By the end of the session, Andriy has walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans who participated in a 2023 randomised controlled trial. Many were demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which was indirect rather than direct clinical cost (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials also rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecast to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and supports a paradigm shift, from a narrow, disease model towards one that values post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to resolve (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high, non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisims that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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[[Category:Motivation and emotion/Book/Psychotherapy]]
[[Category:Motivation and emotion/Book/Trauma]]</text>
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      <text bytes="35819" sha1="9gx0ofb63hylul5zbwq1x9993ce5zez" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy, moves through his 3MDR treatment.

Learn more about immersive therapy and Andriy’s* experience in the chapter below (*Andriy is a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The 2024 World Health Organisation estimates that 3.9% of the world's population has had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017).This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyper arousal (Efremov, 2025; de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hyper-vigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation.'''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue triggering extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) link this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinitely (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, as although emotional regulation contributes substantially to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one that is able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy, towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment and its interaction with the human brain. Designed to give readers a simple understanding of emerging technologies used in immersive PTSD environments.]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]](XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their clinical therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action itself and the cognitive restructuring it enables may be the more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and the actual reality. This may destabilise aspects of the traumatic memory, potentially creating conditions under which memory reconsolidation can occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which taxes limited working memory resources and reduces the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations, who show some of the highest treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the relatively recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional Exposure'''
| valign=&quot;top&quot; |'''Immersive Approach'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Therapeutic Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''
'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing''' '''and attention'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
High dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy* a volunteer in the Ukrainian Armed Forces is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind stays in a constant state of combat readiness, even in a quiet room.

In the pre-platform phase of 3MDR, Andriy worked to identify a ‘hotspot’ memory in a photograph. On the treadmill, harnessed and walking beside his therapist, he faces a panoramic screen as personalised warm-up music plays, selected to keep him in touch with his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy moves through his 3MDR treatment.

By the end of the session, Andriy has walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans who participated in a 2023 randomised controlled trial. Many were demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which was indirect rather than direct clinical cost (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials also rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecast to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to resolve (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high, non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

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}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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[[Category:Motivation and emotion/Book/Trauma]]</text>
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      <text bytes="35805" sha1="34imbqowmu2k5icpwdd5bl4ho4w8xru" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy, moves through his 3MDR treatment.

Learn more about immersive therapy and Andriy’s* experience in the chapter below (*Andriy is a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The 2024 World Health Organisation estimates that 3.9% of the world's population has had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyperarousal (Efremov, 2025; de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinitely (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes substantially to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one that is able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment and its interaction with the human brain. Designed to give readers a simple understanding of emerging technologies used in immersive PTSD environments.]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their clinical therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action itself and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and the actual reality. This may destabilise aspects of the traumatic memory, potentially creating conditions under which memory reconsolidation can occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax limited working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the relatively recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional Exposure'''
| valign=&quot;top&quot; |'''Immersive Approach'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Therapeutic Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''
'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing''' '''and attention'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
High dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy* a volunteer in the Ukrainian Armed Forces is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind stays in a constant state of combat readiness, even in a quiet room.

In the pre-platform phase of 3MDR, Andriy worked to identify a ‘hotspot’ memory in a photograph. On the treadmill, harnessed and walking beside his therapist, he faces a panoramic screen as personalised warm-up music plays, selected to keep him in touch with his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy moves through his 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans who participated in a 2023 randomised controlled trial. Many were demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials also rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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      <text bytes="35561" sha1="227svznp36zqqmdy43cvrv7rgss0sut" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinitely (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes substantially to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one that is able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their clinical therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action itself and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and the actual reality. This may destabilise aspects of the traumatic memory, potentially creating conditions under which memory reconsolidation can occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax limited working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the relatively recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue-delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy* a volunteer in the Ukrainian Armed Forces is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind stays in a constant state of combat readiness, even in a quiet room.

In the pre-platform phase of 3MDR, Andriy worked to identify a ‘hotspot’ memory in a photograph. On the treadmill, harnessed and walking beside his therapist, he faces a panoramic screen as personalised warm-up music plays, selected to keep him in touch with his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy moves through his 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans who participated in a 2023 randomised controlled trial. Many were demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials also rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
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[[Category:Motivation and emotion/Book/Trauma]]</text>
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      <text bytes="35487" sha1="hz1gqvasojcoyy6r92ew3z25zmbbmgl" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3. PTSD can have a deep and lasting impact on our emotions.''']]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests that recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage this intense distress, many individuals adopt a cognitive and behavioural avoidance defence mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires safely reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never safely confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist indefinitely (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes substantially to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one that is able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, highly interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is the concept of how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond the simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their clinical therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action itself and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association actively competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and the actual reality. This may destabilise aspects of the traumatic memory, potentially creating conditions under which memory reconsolidation can occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax limited working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of the VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect used in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical standard trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this broader improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces the recovery process (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the relatively recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue-delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the average annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be best read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials also rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can also disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost an estimated US$3,500 per provider headset annually, and advanced simulation environments can cost up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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      <text bytes="35246" sha1="ax3jmi82i1wxg4rg302cn29hvu6mz2b" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt a cognitive and behavioural avoidance mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue-delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] 
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[w:United_States_Department_of_Veterans_Affairs|United States Department of Veterans Affairs]]
* [[University of Canberra]] 
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
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Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

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Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

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Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

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Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

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}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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      <text bytes="35041" sha1="h0yq1bdvr77sld5v1i6dkb9u39zjwy1" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping an individual in a cycle of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image and expects:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates an opportunity for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please pause and predict the answer before opening this section}}The correct answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
The mismatch between expected danger and actual safety creates a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt a cognitive and behavioural avoidance mechanism (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on concepts by Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by R. Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue-delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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      <text bytes="34980" sha1="9l0e9y8ud1qcpss7sfkwk1y07ow8p55" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping individuals in cycles of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states (Figure 3) (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image expecting:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates opportunities for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please consider the answer before opening this section}}The answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
Mismatches between expected and actual danger create a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt cognitive and behavioural avoidance mechanisms (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on: Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by Selvakumaran (University of Canberra) explores cultural factors using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face to face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring,  questions relevant to both basic and applied research and that current trial designs have not yet addressed.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue-delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing trauma memories need to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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[[Category:Motivation and emotion/Book/Psychotherapy]]
[[Category:Motivation and emotion/Book/Trauma]]
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      <text bytes="35022" sha1="n3bzn4q2ea737pozdil7718yhau1s4x" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping individuals in cycles of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states (Figure 3) (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image expecting:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates opportunities for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please consider the answer before opening this section}}The answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
Mismatches between expected and actual danger create a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt cognitive and behavioural avoidance mechanisms (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on: Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by Selvakumaran (University of Canberra) examining cultural adaptation using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face-to-face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring. These questions relevant to both basic and applied research and have not yet been adequately addressed by current trial designs  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind remains in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing necessary for traumatic memories to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
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      <text bytes="35035" sha1="48tr30g19p1fwjcdwzpdxycsj6lwmdp" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping individuals in cycles of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image expecting:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates opportunities for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please consider the answer before opening this section}}The answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
Mismatches between expected and actual danger create a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt cognitive and behavioural avoidance mechanisms (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on: Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by Selvakumaran (University of Canberra) examining cultural adaptation using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face-to-face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring. These questions relevant to both basic and applied research and have not yet been adequately addressed by current trial designs  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind remains in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this growth, market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing necessary for traumatic memories to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Stratistics MRC. (2025). ''Virtual reality therapy for PTSD market forecasts to 2032: Global analysis by component (hardware, software and service), therapy type, application, end user and by geography.'' https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Psychotherapy]]
[[Category:Motivation and emotion/Book/Trauma]]
&lt;references /&gt;</text>
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      <comment>/* What are the costs and limitations of immersive therapies? */ Removed the Stratistics MRC 2025 industry report from the references and moved it to external links. As the reference is not peer-reviewed and the methodology is private, I've amended the paragraph slightly to soften it. I'm being cautious about treating the analysis as fact - just a useful financial forecast that reflects potential market growth and trends.</comment>
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      <text bytes="35075" sha1="n6ei1trhzliu380qi8fo3qfnlda8mhc" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping individuals in cycles of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image expecting:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates opportunities for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please consider the answer before opening this section}}The answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
Mismatches between expected and actual danger create a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt cognitive and behavioural avoidance mechanisms (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on: Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by Selvakumaran (University of Canberra) examining cultural adaptation using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face-to-face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring. These questions relevant to both basic and applied research and have not yet been adequately addressed by current trial designs  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind remains in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this potential growth trend, some market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing necessary for traumatic memories to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Web:''' [https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market Virtual reality therapy for PTSD market forecasts to 2032:] (Stratistics MR&lt;nowiki/&gt;C, a 2025 industry market report). &lt;nowiki&gt;https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market&lt;/nowiki&gt;
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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      <text bytes="34984" sha1="j9jr8twvoba2lxhmsh1glehjx4lre0u" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping individuals in cycles of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image expecting:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates opportunities for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please consider the answer before opening this section}}The answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
Mismatches between expected and actual danger create a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt cognitive and behavioural avoidance mechanisms (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on: Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by Selvakumaran (University of Canberra) examining cultural adaptation using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face-to-face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring. These questions relevant to both basic and applied research and have not yet been adequately addressed by current trial designs  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind remains in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this potential growth trend, some market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing necessary for traumatic memories to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Web:''' [https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market Virtual reality therapy for PTSD market forecasts to 2032:] (Stratistics MR&lt;nowiki/&gt;C, a 2025 industry market report). 
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

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      <text bytes="34989" sha1="lk5f0wq0ntxqtyc1332v24oon81bhho" xml:space="preserve">{{title|Immersive therapy for PTSD treatment:&lt;br&gt;How does it work and what are the effects?}}
__TOC__
== Overview ==
{{RoundBoxTop|theme=2}}
'''Scenario: Immersive PTSD therapies'''

Andriy, a soldier, harnessed to a treadmill, walks towards an image he spent months avoiding, his clinical therapist  beside him. This is multi-modular motion assisted memory desensitisation and reconsolidation (3MDR), one of a new generation of immersive therapies for post-traumatic stress disorder. 
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 1.''' Andriy moves through his 3MDR treatment.

Learn about immersive therapy and Andriy’s* experience below (*Andriy: a fictional name). {{RoundBoxBottom}}
[[File:Post-traumatic_stress_disorder_world_map_-_DALY_-_WHO2004.svg|alt=|thumb|271x271px|'''Figure 2:''' The World Health Organisation (2024) estimated that 3.9% of the world's population had PTSD at some stage.&lt;ref&gt;{{Cite web|url=https://www.who.int/news-room/fact-sheets/detail/post-traumatic-stress-disorder|title=Post-traumatic stress disorder|website=www.who.int|language=en|access-date=2026-08-17}}&lt;/ref&gt;]]
[[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]] (PTSD) develops after severe or life-threatening trauma and carries a substantial personal and societal cost (Figure 2), with military personnel disproportionately represented (Boska et al., 2025). See costs and limitations below (Davis et al., 2022; Montgomery-Marks et al., 2025). 

PTSD's emotional impact is shaped by [[w:Emotional_dysregulation|emotional dysregulation]] - difficulty managing intense feelings such as guilt, fear or shame (Westphal et al., 2017). This commonly triggers [[Cognitive psychology|cognitive]] and behavioural avoidance that offers short-term relief but prevents traumatic memory from being adaptively processed, trapping individuals in cycles of avoidance and chronic hyperarousal (de Haart et al., 2026; van Gelderen et al., 2018).

Immersive interventions, including [[w:Virtual_reality_therapy|virtual reality exposure therapy]] (VRET) and 3MDR, aim to break this avoidance cycle by creating controlled environments in which trauma cues can be safely approached rather than avoided (van Gelderen et al., 2018; Wiederhold &amp; Wiederhold, 2025). This chapter explains the psychological theory behind these approaches, reviews the research evidence for their effects and considers their limitations.

{{RoundBoxTop|theme=2}}
'''Focus questions'''[[File:Crystal Clear app ktip.svg|left|20px|]]

* Why is emotional processing important in PTSD?
* How can immersive therapies influence the emotional processes underlying PTSD? 
* What does the research evidence show?
* What are the costs and limitations of immersive therapies? 
{{RoundBoxBottom}}

== Why is emotional processing important in PTSD? ==
[[File:PTSD.png|thumb|'''Figure 3.''' PTSD can deeply affect our emotions.]]PTSD is formally diagnosed according to [[w:DSM-5|DSM-5]] criteria and is characterised by disrupted executive and emotional processing systems, heightened threat perception, hypervigilance and persistent negative emotional states as depicted in Figure 3 (Kukharuk et al., 2025; López-Ojeda &amp; Hurley, 2022; Osman et al., 2016). Emotional processing theory provides the primary framework for understanding this disruption, supported by emotion regulation theory and inhibitory learning models introduced later in the chapter.

{{RoundBoxTop|theme=3}}[[Image:Crystal Clear app help index.svg|left|50px]]
;Predict the outcome

A soldier with PTSD encounters a trauma-related image expecting:

'''TRAUMA CUE → DANGER → DISTRESS → AVOID'''

However, during immersive treatment, the expected danger does not occur. What is the most likely consequence?&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
- Fear increases permanently.

- Memory cannot change.

+ Prediction error creates opportunities for new learning.

- Emotional processing stops. 

}

&lt;/quiz&gt;
&lt;div style=&quot;text-align:right; color:red; font-weight:bold;&quot;&gt;
Click &quot;show&quot; below  to understand more⤵ &lt;/div&gt;
{{Hidden begin|title=Please consider the answer before opening this section}}The answer is '''C'''.
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
Mismatches between expected and actual danger create a
'''prediction error'''. This may contribute to fear extinction,
emotion regulation, and memory reconsolidation. '''Think about it:''' If approaching rather than avoiding trauma can create new learning, what role might emotion regulation, fear extinction, prediction error and memory reconsolidation play?
&lt;/div&gt;

 
{{Hidden end}}
&lt;div style=&quot;text-align:left; color:black; font-weight:regular;&quot;&gt;
&lt;/div&gt;{{RoundBoxBottom}}

=== Understanding PTSD and emotions ===
Emotional processing theory suggests recovery requires the trauma memory to be reactivated and updated with corrective information. In PTSD, this process is blocked and to manage distress, many individuals adopt cognitive and behavioural avoidance mechanisms (López-Ojeda &amp; Hurley, 2022). Avoidance offers short-term relief, but prevents the traumatic memory from being reactivated, so it cannot be updated. Trauma reminders such as flashbacks continue to trigger extreme distress, trapping the individual in a maladaptive, self-reinforcing avoidance cycle (Figure 4)  (Vermetten, Burback, et al., 2025b). 

At a neural level, Westphal et al. (2017) linked this to [[wikipedia:Transdiagnostic_process|transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]], in which the traumatic memory network remains isolated from the brain's [[w:Salience_network|salience]]  and central executive networks. Effective treatment requires reactivating this network so the memory can be integrated (Vermetten, Burback, et al., 2025b; Westphal et al., 2017). This is empirically supported: A 2025 study of Danish military veterans (''n''=142) found emotional regulation difficulties explained an additional 28% of the variance in PTSD symptoms; combined with [[w:Comorbidity|comorbid]] symptoms, these factors accounted for 52% of the variance in severity (''F''(13, 92) = 9.58, ''p'' &lt;0.001) (Elklit &amp; Dahl, 2025).[[File:Avoidance and Processing Cycles.png|500x500px|thumb|'''Figure 4'''. Avoidance cycles and the anticipated positive responses associated with immersive therapies. Based on: Lopez-Ojeda et al. (2022), Felemban et al. (2026), and Vermetten et. al. (2025b).|center]]

=== Why treatment can be difficult ===
Trauma-focused psychotherapies such as [[w:Prolonged_exposure_therapy|prolonged exposure]] (PE) and [[w:Cognitive_processing_therapy|cognitive processing therapy]] (CPT) ask patients to actively engage with distressing memories to generate fear extinction, precisely what avoidance prevents (van Toorenburg et al., 2020). Many patients cannot tolerate the emotional exposure these therapies require (Lopes et al., 2025; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Because the trigger is never confronted, the brain cannot experience a prediction error needed to learn the threat has passed, so symptoms persist (de Haart et al., 2026; López-Ojeda &amp; Hurley, 2022).

This is reflected in outcomes where an estimated 39.2% of patients fail to respond to standard trauma-focused therapy, and dropout rates range from 16-48% (de Haart et al., 2026; Vermetten, Burback, et al., 2025b). Among military veterans, younger patients show heightened severity when trauma is central to their identity, while others turn to poor diet or substance abuse, further eroding emotional regulation (Efremov, 2025; Niles et al., 2023).

[[w:Emotional_dysregulation|Emotional dysregulation]] was historically viewed as a fixed barrier requiring lengthy stabilisation before treatment could begin (van Toorenburg et al., 2020). More recent evidence suggests otherwise, although emotional regulation contributes to PTSD symptoms, it is also being increasingly viewed as a modifiable process with dynamic capacity, one able to improve as a natural consequence of successful memory processing (van Toorenburg et al., 2020). This reframes the clinical challenge as helping an individual safely approach and process the traumatic memory, not correcting a fixed deficit. [[File:UC PhD VR study.png|right|thumb|'''Figure 5.''' PhD work by Selvakumaran (University of Canberra) examining cultural adaptation using the US-''Bravemind'' system.]]Cultural context adds another layer of difficulty. Doctoral research at the [[University of Canberra]] is examining how protocols such as the US-centric ''Bravemind''&lt;ref&gt;{{Cite web|url=https://medvr.ict.usc.edu/projects/bravemind.html|title=Bravemind {{!}} MedVR|website=medvr.ict.usc.edu|access-date=2026-08-25}}&lt;/ref&gt; need cultural adaptation for Australian veterans and first responders, whose operational backgrounds differ from their US counterparts (Selvakumaran, 2025). Integrating exposure therapy with gamified, posture-adaptive cognitive rehabilitation to support physical and emotional recovery (Figure 5)  (Selvakumaran, 2025). These treatment gaps carry a substantial economic and personal cost, part of the motivation for developing alternatives such as immersive therapies.   

== How can immersive therapies influence emotional processes? ==
Immersive PTSD treatments mark a shift from passive, sedentary therapy towards active, embodied, interactive approaches (van Gelderen et al., 2018). Immersive therapy uses three psychological mechanisms and their interaction: multisensory presence, embodied cognition, and divergent thinking (López-Ojeda &amp; Hurley, 2022; van Gelderen et al., 2018).

Embodied cognition is how physical states of the body can directly modify states of the mind (van Gelderen et al., 2018). Immersion therapy goes beyond simple visual replication of a trauma memory; instead, capturing the participant’s visceral and cognitive focus by limiting distractions (Macey et al., 2026). 

=== What is immersive therapy? ===
[[File:XR and Human Senses.png|right|thumb|'''Figure 6.''' The Extended Reality environment. ]]Immersive therapies&lt;ref&gt;{{Cite journal|date=2026-06-01|title=Immersion therapy|url=https://en.wikipedia.org/w/index.php?title=Immersion_therapy&amp;oldid=1357152847|journal=Wikipedia|language=en}}&lt;/ref&gt; use [[w:Extended_reality|extended reality]] (XR) platforms, encompassing [[virtual reality]] (VR), [[Augmented Reality|augmented reality]] (AR), and [[w:Mixed_reality_game|mixed reality]] (MR), to create customisable, controlled, and standardised therapeutic environments (López-Ojeda &amp; Hurley, 2022; Wiederhold &amp; Wiederhold, 2025). This ecosystem is depicted in Figure 6.
This chapter focuses on two applications: VRET where therapists reconstruct traumatic scenarios in safe, graded environments, and 3MDR, which extends this by having the patient move on a treadmill beside their therapist, rather than in a stationary, face-to-face session (de Haart et al., 2026; Felemban et al., 2026).

=== Presence and embodied cognition ===
Immersive therapy’s distinguishing feature is its ability to generate presence, or the psychological illusion of being ‘''there’''. The illusion is amplified by integrating synchronised audio, visual, olfactory, haptic, and movement stimuli (Lopes et al., 2025; López-Ojeda &amp; Hurley, 2022). This increases engagement with the trauma memory and supports emotional processing (van Gelderen et al., 2018).

In 3MDR, presence combines with cognition. The working principle is that physical states of the body can directly shape states of the mind (van Gelderen et al., 2018). Walking towards a virtual trauma reminder functions as a fear antagonistic action and rather than retreating in avoidance, the patient approaches, converting passive helplessness into active, empowered participation and disrupting the rigid and repetitive trauma narratives  common in PTSD (de Haart et al., 2026; Osman et al., 2016; van Gelderen et al., 2018). 

Notably, extinction learning normally requires moderate-to-high-intensity activity to stimulate [[w:Brain-derived_neurotrophic_factor|brain-derived neurotrophic factor]] (BDNF), but 3MDR's walking pace (&lt; 4 km/h) is too slow to generate meaningful BDNF secretion, making a major exercise induced BDNF mechanism unlikely, although physiological factors cannot be ruled out. The approach action and the cognitive restructuring it enables may be more important psychological drivers (de Haart et al., 2026).

=== Prediction error and inhibitory learning ===
Immersive therapy builds on the inhibitory learning model of exposure therapy, in which a new, safe association competes with and suppresses the original fear response. Walking towards a trauma cue and encountering safety instead of the expected catastrophe creates a prediction error between the anticipated, life-threatening event and actual reality. This may destabilise the traumatic memory, potentially creating conditions for memory reconsolidation to occur (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

=== Memory reconsolidation ===
According to [[w:Memory_consolidation|memory reconsolidation]] theory, traumatic memories retrieved in a safe immersive context can become [[w:Malleability_of_intelligence|malleable]], allowing new, safe information to reconsolidate the memory in a non-threatening form (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). To prevent the patient from becoming overwhelmed, 3MDR uses dual-attention tasks such as tracking an oscillating ball (Figure 1), which tax working memory resources and reduce the vividness and emotional intensity of the memory (Vermetten, Burback, et al., 2025b).

Emerging linguistic research suggests this processing is reflected in patients' language. Across successive 3MDR sessions, [[w:Affect_labeling|affective labelling]] of feelings such as guilt shifted from past-tense to present-tense narration, consistent with a renewed ability to integrate traumatic memories into present-moment awareness (Vermetten, Barcaro, et al., 2025a).

== What does the research evidence show? ==
Addressing these barriers is important for any PTSD population, but especially critical for military populations with high treatment failure and dropout rates (van Gelderen et al., 2018). Immersive therapies can tailor patient-selected trauma cues to improve access to traumatic memory networks (Vermetten, Burback, et al., 2025b). 

=== Virtual reality exposure therapy ===
[[w:Virtual_reality_therapy|VRET]] reconstructs traumatic events in a structured context (Felemban et al., 2026; López-Ojeda &amp; Hurley, 2022). This may help bypass imagination challenges such as emotional numbing or amnesia that can prevent patients from engaging with traditional therapy (Macey et al., 2026). A meta-analysis of VRET for PTSD found substantial symptom reductions, averaging a 33.73-point decrease in the 0-80 point [[w:Clinician_Administered_PTSD_Scale|Clinician-Administered PTSD Scale]] and a 20.96-point decrease in the 0-80 point [https://www.ptsd.va.gov/professional/assessment/adult-sr/ptsd-checklist.asp PTSD Checklist PCL-5) scale]  (Felemban et al., 2026). Because changes of 10-20 points on these scales are considered clinically significant, this could mean the difference between severe functional impairment and mild or subclinical symptoms (Boska et al., 2025; de Haart et al., 2026; Felemban et al., 2026).  Comparative effects against other active PTSD treatments remain modest, but VRET appears to be a more engaging alternative to conventional treatment (Felemban et al., 2026)

=== 3MDR ===
3MDR takes the same multisensory effect in VRET and adds an activating context. Rather than a sedentary, face-to-face session, the patient and the therapist face the virtual display together (van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). It follows a three-phase protocol: pre-platform preparation, platform treadmill exposure, and post-platform re-consolidation (Vermetten, Burback, et al., 2025b). In a trial involving treatment-resistant PTSD; 3MDR showed large effect sizes from pre-treatment to six-months (''n'' = 134, ''d'' = 1.0) and high-acceptability, with 7-20% dropout rates (de Haart et al., 2026; van Gelderen et al., 2018; Vermetten, Burback, et al., 2025b). Substantially lower than the 16-48% typical trauma-focused therapy in military populations (Lewis et al., 2020).

Improvements are not limited to PTSD symptoms. A trial of 62 adults with severe PTSD, including childhood sexual trauma, found intensive trauma-focused treatment improved emotion-regulation abilities regardless of PTSD outcome (van Toorenburg et al., 2020). Some researchers link this improvement to positive psychology [[w:Broaden-and-build|Broaden-and-Build Theory]]. Theorising that as patients regain a sense of safety and control, this may support a positive spiral of emotional flexibility that reinforces recovery (Fredrickson, 2001; Niles et al., 2023; Westphal et al., 2017).  

Critically, the exact causation remains unknown. Given the recent innovations in immersive therapies and small study samples, it remains unclear whether they work through exposure-based extinction, enhanced emotional engagement, physiological factors, embodiment or positive cognitive restructuring. These questions are relevant to both basic and applied research and have not yet been adequately addressed by current trial designs.  

'''Table 1:''' Treatment effects and psychological mechanisms
{| class=&quot;wikitable mw-collapsible&quot;
| valign=&quot;top&quot; |'''Clinical Dimension'''
| valign=&quot;top&quot; |'''Traditional'''
| valign=&quot;top&quot; |'''Immersive'''
| valign=&quot;top&quot; |'''Psychological Mechanisms'''
|-
| valign=&quot;top&quot; |'''Context'''
| valign=&quot;top&quot; |'''''Sedentary'''''. Face-to-face, verbally describes trauma.
| valign=&quot;top&quot; |'''''Activating.''''' Dynamic, multi-sensory environment.
| valign=&quot;top&quot; |'''''Fear Antagonistic Action.'''''
'''''Approach behaviours.'''''

'''''Prediction Errors.'''''
|-
| valign=&quot;top&quot; |'''Trauma cue delivery'''
| valign=&quot;top&quot; |'''''Imaginary Retrieval'''''
Patient capacity
| valign=&quot;top&quot; |'''''Multisensory Immersion'''''
Highly tailored
| valign=&quot;top&quot; |'''''External Scaffolding.'''''
Bypasses internal barriers to activate memory networks.
|-
| valign=&quot;top&quot; |'''Processing'''
| valign=&quot;top&quot; |'''''Convergent processing.'''''
Repeated narration and fear habituation.
| valign=&quot;top&quot; |'''''Active Narrative Processing.'''''
Interactive, real-time affective labelling and dual attention tasks.
| valign=&quot;top&quot; |'''''Working Memory.'''''
Memory taxation reduces vividness and emotional intensity.
|-
| valign=&quot;top&quot; |'''Engagement''' 
| valign=&quot;top&quot; |'''''Attrition.'''''
Dropout rates 16-48%.
| valign=&quot;top&quot; |'''''Acceptability.'''''
Attractive. Dropout rates 7-20%.
| valign=&quot;top&quot; |'''''Sustained Motivation.'''''
Presence and safety in immersive environment.
|}
=== Applied example: 3MDR treatment in Ukraine ===
{{RoundBoxTop|theme=2}}
'''Scenario: Ukraine War: an applied 3MDR example'''

Andriy*, a Ukrainian Armed Forces volunteer, is struggling with hyper-vigilance, anxiety, and depression (Kukharuk et al., 2025). Traditional ‘talk’ therapy feels impossible; his mind remains in a constant state of combat readiness, even in quiet rooms.

In the pre-platform phase, Andriy identifies ‘hotspot’ memories in photographs. On the treadmill, harnessed and walking, he faces a panoramic screen as personalised warm-up music plays, selected to keep him connected to his traumatic memory network (Vermetten et al., 2025b). As his hotspot image fills the screen, his therapist asks three questions (Vermetten et al., 2025b):

1. What do you '''SEE''' ?
2. What does it '''TELL''' you?
3. What do you '''FEEL''' in your body NOW?

When Andriy identifies a surge of shame, the word '''GUILT''' is displayed as an affective label, and a dual-attention task begins. He tracks an oscillating, numbered ball while he stays with the emotion, taxing his working memory and reducing the intensity of the recalled trauma.
[[File:Andriy 3MDR enhanced.gif|center|600x600px]]

'''Figure 7.''' Andriy's 3MDR treatment.

By the end of the session, Andriy had walked toward what he used to avoid, creating a mismatch between his expectation of threat and his safety and turning a rigid, stuck memory into a manageable narrative.

*''Andriy, a fictional name given to one of 69 Ukrainian veterans, participating in a 2023 randomised controlled trial. Many demobilised after one year because of mental or neurological injuries'' (Kukharuk et al., 2025). 

{{RoundBoxBottom}}

== What are the costs and limitations of immersive therapies? ==
PTSD carries a substantial economic burden. An estimated US$232 billion in excess costs in the United States in 2018 and over £40 billion, in the United Kingdom in 2020-21, 92.4% of which were indirect rather than direct clinical costs (Davis et al., 2022; Montgomery-Marks et al., 2025). In Australia, the annual cost of PTSD per military veteran was estimated at $112,172 in 2025 (Magnusson &amp; Dey, 2025). In addition, individual healthcare costs surge by 142% in the year following a PTSD diagnosis, with comorbidities tripling this effect (Bothe et al., 2020). These figures span several countries and years and should be read as an indication of scale rather than as directly comparable totals.

Immersive therapy’s ability to move from small trials into mainstream PTSD treatment remains limited by methodological [[w:Homogeneity_and_heterogeneity|heterogeneity]], small sample sizes, and a lack of long-term data (Felemban et al., 2026). Many trials rely on military-heavy, treatment-resistant samples with few active comparison conditions, which limits the generalisation of findings to civilian or initial treatment populations.   Practical issues such as [[w:Virtual_reality_sickness|cyber sickness]] or motion sickness can disrupt participation (Kukharuk et al., 2025).

Structural barriers include workforce training and equipment costs. Basic VR systems cost around US$3,500 per provider headset annually, with advanced simulation environments costing up to US$200,000 (Garrett et al., 2018). Despite this, adoption of immersive therapy is scaling. The [[w:United_States_Department_of_Veterans_Affairs|United States Veterans Affairs]] have expanded VR use from five medical centres in 2017 to over 154 centres and 2,300 staff, with applications now including over 40 documented clinical interventions such as chronic pain and suicide intervention (Bailey et al., 2024). Reflecting this potential growth trend, some market analysts estimate the global PTSD-focused VR therapy market was worth US$1.59 billion in 2025, forecasted to reach US$5.94 billion by 2032, driven largely by growing mental health awareness and the absence of standard clinical protocols (Stratistics MRC, 2025, an industry market report).

These limitations do not undermine the case for immersive therapy, but they show its evidence base and infrastructure are still maturing. Demonstrating rigorously why these therapies work, rather than assuming their novelty accounts for their effects is essential to avoid misallocating resources to unproven interventions and may support an emerging shift towards greater emphasis on post-traumatic growth and renewed optimism (Trejo et al., 2015; Vermetten, Burback, et al., 2025b; Wiederhold &amp; Wiederhold, 2025).

{{Robelbox|theme=2|title=Quiz}}
&lt;quiz display=simple&gt;
{Which of the following is an expected outcome of immersive therapy ?
|type=&quot;()&quot;}


- Patients are at risk because of an uncontrolled environment.
- The environments represent traditional face-to-face treatments.
- Failure and dropout rates are higher than traditional PTSD treatment.
+ Patients often broaden and build an upward spiral of emotion and optimism.
&lt;/quiz&gt;
{{Robelbox/close}}
== Conclusion ==
PTSD traps people in a self-reinforcing cycle of avoidance that blocks the adaptive processing necessary for traumatic memories to be resolved (see: ''Understanding PTSD and emotions''). Standard trauma-focused therapies require patients to confront exactly what this cycle causes them to avoid, which contributes to high non-response and dropout rates (see ''Why treatment can be difficult'').

Immersive therapies such as VRET and 3MDR address this by using presence, embodied cognition, prediction error and memory reconsolidation to help patients safely approach trauma cues rather than avoid them (see: ''What does the research evidence show''). The technology itself is only a delivery mechanism that enables the processes, the positive benefits appear to arise from the psychological mechanisms that immersive therapies facilitate, rather than the novelty of technology alone.

The evidence to date shows meaningful reductions in PTSD symptoms and comparatively low drop-out rates, alongside broader gains in emotional regulation. However, small samples, methodological variation, and a lack of long-term data mean the evidence base is still developing, and cost and infrastructure barriers remain significant (see ''costs and limitations'').{{RoundBoxTop|theme=11}}
[[File:Nuvola apps kuser.svg|Nuvola apps kuser|left|20px]] ''' Take-home message:''' 
Immersive therapies do not heal PTSD trauma through technological novelty or digital feedback. Instead, they create a safe, dynamic space that lets individuals confront trauma and reprocess memories into something they can live with. In doing so, people’s lives may once again shift toward value, optimism, and wellness.{{RoundBoxBottom}}

== See also ==
'''Wikiversity'''

* [[Motivation and emotion/Textbook/Emotion/Anxiety|Anxiety book chapter]]
* [[Evidence-based assessment/Posttraumatic stress disorder (disorder portfolio)|Evidence-based PTSD assessment]]
* [[Motivation and emotion/Book/2019/Phobias|Phobias book chapter]] 

* [[Motivation and emotion/Book/2024/Sense hacking|Sense hacking book chapter]] 
'''Wikipedia'''

* [[w:Affect_labeling|Affective labelling]] 
* [[Augmented Reality|Augmented reality]] 
* [[w:Brain-derived_neurotrophic_factor|Brain-derived neurotrophic factor]] 
* [[w:Broaden-and-build|Broaden-and-build theory]]
* [[w:Cognitive_processing_therapy|Cognitive processing therapy]] 
* [[w:Virtual_reality_sickness|Cyber sickness]]
* [[w:DSM-5|DSM-5]]
* [[w:Emotional_dysregulation|Emotional dysregulation]] 
* [[w:Extended_reality|Extended reality]]
* [[w:Malleability_of_intelligence|Malleability of intelligence]] 
* [[w:Memory_consolidation|Memory reconsolidation]]
* [[w:Mixed_reality_game|Mixed reality]] 
* [[w:Post-traumatic_stress_disorder|Post-traumatic stress disorder]]
* [[w:Prolonged_exposure_therapy|Prolonged exposure therapy]] 
* [[wikipedia:Transdiagnostic_process|Transdiagnostic]] [[w:Emotional_dysregulation|emotion dysregulation]]
* [[wikipedia:Virtual_reality_therapy|Virtual reality exposure therapy]]

== References ==
{{Hanging indent|Bailey, A. L., Kirsh, S., Rawlins, C., Persky, S., &amp; Clancy, C. (2024). Early scaling of immersive technology within the Veterans Health Administration. ''NEJM Catalyst Innovations in Care Delivery'', 5(4). https://doi.org/10.1056/cat.23.0356

Boska, R. L., Bishop, T. M., Capron, D. W., Paxton Willing, M. M., &amp; Ashrafioun, L. (2025). Difficulties with emotion regulation within PTSD clusters and moral injury subtypes. ''Military Psychology'', 37(2), 159-167. https://doi.org/10.1080/08995605.2024.2322904

de Haart, R., Daniels, J. K., Timmerman, M. E., Cath, D. C., &amp; Lommen, M. J. J. (2026). Augmenting virtual reality exposure for PTSD with physical activity: Study protocol of a randomised controlled trial. ''European'' ''Journal of Psychotraumatology'', 17(1), 2605803. https://doi.org/10.1080/20008066.2025.2605803

Efremov, A. (2025). Age-specific mental health profiles of combat veterans: Post-traumatic stress disorder and related disorders. ''Journal of Rational-Emotive &amp; Cognitive-Behavior Therapy'', 44(4), 1-15. https://doi.org/10.1007/s10942-025-00637-7

Elklit, A., &amp; Dahl, N. H. (2025). Emotion regulation difficulties, aggression, and PTSD symptoms in Danish treatment-seeking veterans. ''Scandinavian Journal of Military Studies'', 8(1), 308-326. https://doi.org/10.31374/sjms.264

Felemban, R. G., Alzahrani, R. R., Alrefaei, N. F., Alharbi, N. M., Alghamdi, A. S., &amp; Alqadi, S. (2026). Efficacy of virtual reality-based exposure therapy for post-traumatic stress disorder in military veterans: A systematic review and meta-analysis. ''Frontiers in Psychiatry'', 17, 1857109. https://doi.org/10.3389/fpsyt.2026.1857109

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. ''American Psychologist'', 56(3), 218-226. https://doi.org/10.1037/0003-066X.56.3.218

Garrett, B., Taverner, T., Gromala, D., Tao, G., Cordingley, E., &amp; Sun, C. (2018). Virtual reality clinical research: Promises and challenges. ''JMIR Serious Games'', 6(4), e10839. https://doi.org/10.2196/10839

Kukharuk, O., Tkalich, K., Kamash, N., &amp; Georgiou, O. (2025). Effectiveness of immersive VR therapy in reducing stress-associated symptoms in Ukraine. ''European Journal of Psychotraumatology'', 16(1), 2488097. https://doi.org/10.1080/20008066.2025.2488097

Lewis, C., Roberts, N. P., Andrew, M., Starling, E., &amp; Bisson, J. I. (2020). Psychological therapies for post-traumatic stress disorder in adults: Systematic review and meta-analysis. ''European Journal of Psychotraumatology'', 11(1), 1729633. https://doi.org/10.1080/20008198.2020.1729633

Lopes, M. K. S., Perreault, L., de Jesus, B. Jr., Roberge, M. C., &amp; Falk, T. H. (2025). Subjective and objective evaluation of the benefits of multisensory virtual nature immersion for patients with post-traumatic stress disorder. In ''Proceedings of the 17th International Conference on Quality of Multimedia Experience'' (QoMEX) (pp.1-5). IEEE. https://doi.org/10.1109/QoMEX65720.2025.11219945

López-Ojeda, W., &amp; Hurley, R. A. (2022). Extended reality technologies: Expanding therapeutic approaches for PTSD. ''The Journal of Neuropsychiatry and Clinical Neurosciences'', 34(1), 1-5. https://doi.org/10.1176/appi.neuropsych.21100244

Macey, A.-L., Macey, J., &amp; Hamari, J. (2026). Emotion regulation in immersive virtual reality environments: A scoping review. ''Interacting with Computers'', 29, 1-20. https://doi.org/10.1093/iwc/iwag029

Niles, B., Lang, A., &amp; Olff, M. (2023). Complementary and integrative interventions for PTSD. ''European Journal of Psychotraumatology'', 14(2), 2247888. https://doi.org/10.1080/20008066.2023.2247888

Osman, A., Paczynski, M., &amp; Jha, A. P. (2016). Affective expectations influence neural responses to stressful images in soldiers. ''Military Psychology'', 29(1), 41-57. https://doi.org/10.1037/mil0000128

Selvakumaran, R. V. (2025). Developing virtual reality (VR) simulations with embedded user analytics for cognitive rehabilitation in PTSD veterans. In ''Proceedings of the 27th International Conference on Multimodal Interaction'' (pp. 740-744). ACM. https://doi.org/10.1145/3716553.3750826

Trejo, B. C., Richard, E. M., van Driel, M., &amp; McDonald, D. P. (2015). Cross-cultural competence: The role of emotion regulation ability and optimism. ''Military Psychology'', 27(5), 276-286. https://doi.org/10.1037/mil0000081

van Gelderen, M. J., Nijdam, M. J., &amp; Vermetten, E. (2018). An innovative framework for delivering psychotherapy to patients with treatment-resistant posttraumatic stress disorder: Rationale for interactive motion-assisted therapy. ''Frontiers in Psychiatry'', 9, 176. https://doi.org/10.3389/fpsyt.2018.00176

van Toorenburg, M. M., Sanches, S. A., Linders, B., Rozendaal, L., Voorendonk, E. M., Van Minnen, A., &amp; De Jongh, A. (2020). Do emotion regulation difficulties affect outcome of intensive trauma-focused treatment of patients with severe PTSD? ''European Journal of Psychotraumatology'', 11(1), 1724417. https://doi.org/10.1080/20008198.2020.1724417

Vermetten, E., Barcaro, S., Espejo, E., Bellini, P., Roy, M. J., &amp; Bremault-Phillips, S. (2025a). Linguistic analysis of patients’ labels during 3MDR psychotherapy. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S29. https://doi.org/10.5152/pcp.2025.241024

Vermetten, E., Burback, L., Sevigny, P. R., Nijdam, M. J., Winkler, O., Espejo, E., Sessoms, P., Bright, K., Roy, M. J., &amp; Brémault-Phillips, S. (2025b). Brief manual for multi-modal motion-assisted memory desensitization and reconsolidation therapy for the treatment of post-traumatic stress disorder. ''Psychiatry and Clinical Psychopharmacology'', 35(Suppl. 1), S122. https://doi.org/10.5152/pcp.2025.241028

Westphal, M., Aldao, A., &amp; Jackson, C. (2017). Emotion dysregulation in comorbid posttraumatic stress disorder and substance use disorders: A narrative review. ''Military Psychology'', 29(3), 216-233. https://doi.org/10.1037/mil0000157

Wiederhold, B. K., &amp; Wiederhold, M. D. (2025). Virtual reality therapy combined with physiological monitoring provides effective treatment, with objective metrics, for post-traumatic stress disorder. ''Expert Review of Medical Devices'', 22(2), 117-119. https://doi.org/10.1080/17434440.2025.2454930
}}


== External links ==
* '''Web:''' [https://www.healthdirect.gov.au/post-traumatic-stress-disorder-ptsd Post traumatic stress disorder] (Australian Government)
* '''Web:''' [https://www.ptsd.va.gov/index.asp National Center for PTSD information home page]  (US Government)
* '''Web:''' [https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html US Veterans Affairs Immersive Programs Innov]&lt;nowiki/&gt;[https://www.innovation.va.gov/hil/views/immersive/immersive-programs.html ation] (US Government)
* '''Web:''' [https://defenceveteransuicide.royalcommission.gov.au/publications/final-report Australian Royal Commission into Defence and Veteran Suicide - Final Repor]&lt;nowiki/&gt;[https://defenceveteransuicide.royalcommission.gov.au/publications/final-report t] (Australian Government)
* '''Web:''' [https://www.strategymrc.com/report/virtual-reality-therapy-for-ptsd-market Virtual reality therapy for PTSD market forecasts to 2032:] (Stratistics MR&lt;nowiki/&gt;C, a 2025 industry market report). 
* '''Podcast:''' [https://shows.acast.com/5c3353e484e2e79370e1d135/5c3353ef84e2e79370e1d13c PTSD Podcast] (Peace of Mind: Mental Health and Psychiatry, ACAST, 43 min)
* '''Video:''' [https://www.youtube.com/watch?v=bD43R_oa6qo 3MDR: Virtual reality treatment for veterans] (National Centre for Mental Health,Youtube, 2:46 min)
* '''Video:'''  [https://www.youtube.com/watch?v=jL2bKmniMTc VR exposure for combat PTSD] (PsyTech VR, Youtube, 2:20 min)  
* '''Final Report:''' [https://www.ncmh.info/wp-content/uploads/2020/05/Cardiff-3MDR-Study-Final-Report-with-cover-21.5.20.pdf 3MDR randomised control trial - Final-Report] (Cardiff University)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Psychotherapy]]
[[Category:Motivation and emotion/Book/Trauma]]
&lt;references /&gt;</text>
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      <text bytes="6311" sha1="nv2dcsz7x2q8qtw7gw3a91zpv39mi8g" xml:space="preserve">== About me ==
Hi, my name is [https://www.linkedin.com/in/pepper-white/ Pepper]. I am a third-year Bachelor of Science in Psychology student at the [https://www.canberra.edu.au/ University of Canberra]. I am passionate about preventative mental health care and supporting those in need. This passion motivates me in my studies and at work.  

=== Work experience ===
* '''Mental Health Educator''' with [https://mieact.org.au/ Mental Illness Education ACT]. In this role,  I facilitate discussions about [[Stress (psychological)|stress]], [https://www.beyondblue.org.au/mental-health/depression?gad_source=1&amp;gad_campaignid=21934835275&amp;gbraid=0AAAAADuibRbKbycJc05RErZ8UMCld1aGB&amp;gclid=Cj0KCQjwkOvTBhDgARIsAKUNyRuK4CGO5WdRCpr1RDshuiDIlyi_ZwRe8ZFfvAygSGrvK0TbjFm7VtYaAkf8EALw_wcB depression], and [[wikipedia:Help-seeking|help-seeking]] with ACT school students. 

* '''Student Advocate''' in the [https://www.canberra.edu.au/content/myuc/home/support/student-advocacy-and-src/student-advocacy.html Student Advocacy Office] at the University of Canberra. In this role, I help my peer university students navigate university policies and procedures. 

=== Hobbies ===
* [[wikipedia:Oil_painting|Oil painting]]
* Figure drawing
* Running
* Playing water polo with the [https://www.revolutionise.com.au/dragonswp/home/ Gungahlin Dragons Water Polo Club]
* Travelling

== Book chapter ==
The book chapter I am writing is [[Motivation and emotion/Book/2026/Self-concept and motivation|Self-concept and motivation]]. The chapter navigates the question &quot;How does self-concept relate to motivation?&quot; I chose this topic to explore due to my fascination with how the perception of oneself can influence one's behaviour.

== Social contributions ==
My approach for social contributions has been to edit or comment on a peer's page every time I work on my own book chapter. My hope is that this approach helps me stay engaged with others' ideas and contribute as regularly to others' work as I do my own.   
# I engaged with conversations in a [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261?entry_id=804001 discussion post] on Canvas about topics of interest within motivation and emotion. My goal with this post was to take inititative by being an early contributor to help build a sense of comfort and normality amongst the group. I also hope by posting some topics of interest, others may feel inspired by these focus areas, thus helping them choose their book chapter topic.
# In familiarising myself with Wikiversity, I read the Spirituality and resilience 2025 book chapter. I noticed the writing required edits for readability, so I [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FSpirituality_and_resilience&amp;diff=2824208&amp;oldid=2774009 edited the first two paragraphs] of the overview. I fixed spelling, grammar, and wording issues. This is an important fix to help capture the reader’s attention and demonstrate credibility when the audience begins reading.
# I went through the topics others have chosen and the topic “Empathy and jury decision-making&quot; caught my attention. I [https://en.wikiversity.org/w/index.php?title=Talk%3AMotivation_and_emotion%2FBook%2F2026%2FEmpathy_and_jury_decision-making#Exploring_empathy_within_similar_contexts commented] on this book chapter with some additional ideas from my own passion about researching empathy to support this students’ topic development.
# To better illustrate the multidimensional model of self-concept Marsh et al. (1992), which I refer to in my book chapter, I [https://commons.wikimedia.org/w/index.php?title=File%3AMultidimensional_model_of_self-concept_diagram.png&amp;diff=1265404333&amp;oldid=1265404322 created a diagram and uploaded it to Wikimedia].
# I looked through the book chapter &quot;Empathy and jury decision-making&quot; and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEmpathy_and_jury_decision-making&amp;diff=2826959&amp;oldid=2824982 made edits] to the ordering of citations within a bracket in the conclusion to ensure they were alphabetical.
# I read the book chapter &quot;Falling in love&quot; and [https://en.wikiversity.org/w/index.php?title=Talk%3AMotivation_and_emotion%2FBook%2F2026%2FFalling_in_love#Interesting_theories_to_incorporate suggested a few theories and angles to explore] within this fascinating topic.
# I read the book chapter &quot;Charismatic leadership and follower motivation&quot; and [[Talk:Motivation and emotion/Book/2026/Charismatic leadership and follower motivation#Interesting real-life case study to consider incorporating|suggested exploring the Jonestown cult]] as a real life case study to give insight into the extreme side of charismatic leadership and follower motivation.
# To connect with others also writing 'self-' related chapters, I read the book chapter &quot;Possible selves and goal pursuit&quot;. I identified areas which may require more research and [[Talk:Motivation and emotion/Book/2026/Possible selves and goal pursuit#c-U3253363-20260909032900-Jshottt-20260827141800|posted on their discussion forum]] some of the research I have been using which could be relevant to their chapter.
# I reviewed the book chapter &quot;Love styles and relationship satisfaction&quot; and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FLove_styles_and_relationship_satisfaction&amp;diff=2832497&amp;oldid=2759229 made stylistic and grammatical edits throughout,] in particular I fixed capitalisation to sentence casing in headings and fixed the broken Wiki links.
# I [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/461216?entry_id=816875 suggested an easy and new way to check your chapter's word count] in a Canvas discussion board.
# In reviewing a chapter of interest to me, Volunteer counsellor motivation: Difference between revisions, I noticed the scenario being used did not involve a made up person or factual story, it instead had an introduction to a theory. To help the author catch the reader's attention, I [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FVolunteer_counsellor_motivation&amp;diff=2833605&amp;oldid=2832761 added a suggestion for a scenario] which involves a concrete case and a real person to help the reader connect immediately with the chapter.</text>
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      <text bytes="32272" sha1="fua5h51d9qw9cr9v0igvu1nvd9oma7k" xml:space="preserve">{{title|Emotional intelligence:&lt;br&gt;How does emotional intelligence affect emotional wellbeing?}}
__TOC__

== Overview ==
{{RoundBoxTop|theme=3}}
[[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]]

'''Scenario'''

Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict.

Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively.

Why might people respond so differently to similar emotional situations?

One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing.

Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically.

Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship.

{{RoundBoxBottom}}
* {{RoundBoxTop}}
; Focus questions
# What are emotional intelligence and emotional wellbeing? 
# What is the relationship between emotional intelligence and emotional wellbeing?
# How does emotional intelligence influence emotional wellbeing?
#Which components of emotional intelligence are particularly important for emotional wellbeing?
# How can emotional intelligence be developed to support emotional wellbeing?

{{RoundBoxBottom}}

== What are emotional intelligence and emotional wellbeing? ==
Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood.

=== Defining emotional intelligence ===
Emotional intelligence describes how people process and manage emotional information  noticing emotional cues, making sense of what they mean, and using that understanding to guide thought and behaviour (Givon et al., 2020).This is a somewhat different idea from how the term emotional is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be equated with simply being a nice person. Kindness reflects a disposition or value, whereas EI reflects an ability; a person can be highly emotionally intelligent while still setting firm boundaries or delivering difficult feedback, and a person can be warm and agreeable while struggling to accurately identify or regulate their own emotions (Salovey &amp; Grewal, 2005). Someone can therefore be outwardly calm and reserved while processing emotional information very effectively, just as someone can be outwardly expressive while struggling to understand or manage what they feel (Villanueva et al., 2020).

Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. As already noted, ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness.

These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models.

==== '''Table 1. Ability model of emotional intelligence''' ====
{| class=&quot;wikitable&quot;
!Branch
!Description
|-
|'''Perceiving emotions'''
|Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language.
|-
|'''Using emotions to facilitate thought'''
|Harnessing emotional information to guide attention, reasoning, and problem-solving.
|-
|'''Understanding emotions'''
|Comprehending emotional causes, consequences, and the way emotions change or combine over time.
|-
|'''Managing emotions'''
|Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing.
|}


Each branch can support wellbeing in its own way. Accurately noticing emotions helps people recognise what they and others feel. Using emotions to support thinking means letting feelings guide attention and judgment. Understanding emotions helps people figure out why emotions happen and how they change. Managing emotions is about handling emotional responses, which is especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend.

Explain the four branches:

# Perceiving emotions
# Using emotions to facilitate thought
# Understanding emotions[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]Managing emotions

Explain briefly how each ability could theoretically contribute to wellbeing.

&lt;quiz display=&quot;simple&quot;&gt;
Quiz 1. 
Which statement best describes emotional intelligence?
|type=&quot;()&quot;}
+ The ability to perceive, understand, use, and manage emotions.
- The ability to avoid experiencing negative emotions.
- The ability to remain happy in all situations.
- The ability to control the emotions of other people.
}
&lt;/quiz&gt;

=== Trait emotional intelligence ===
Trait EI focuses on how people see their own emotional abilities and tendencies, rather than how they perform on objective tests. Self-report measures of EI reflect trait EI in the same way that personality tests show personality traits and patterns. Cronbach explained that self-report and performance-based tests are different because they measure different things: how someone usually acts, versus their best possible performance. Self-report measures show a person's typical emotional functioning, while performance-based tests try to measure their highest ability under test conditions. Cronbach also pointed out that this is a helpful way to understand the difference, not a complete theory; self-report tests can still reveal real skills and abilities, and performance-based tests don't always bring out someone's true best performance either.

Chapman (2005) frames this debate as a question of where emotional intelligence fits within established personality and ability frameworks. For example, psychologists often use the Big Five to organise personality traits. In this view, trait EI is more closely related to personality taxonomies, while ability EI is more like cognitive ability taxonomies. This difference helps explain why researchers measure the two differently.A range of self-report instruments have been developed to assess trait EI. Two commonly used measures are the Trait Meta-Mood Scale, which looks at how well someone notices, understands, and manages their own moods, and the Schutte Self-Report Inventory of Emotional Intelligence , which has held up well in terms of reliability and accuracy in research.

Trait EI is measured through self-report, so it only shows how people view their own emotional intelligence. People may be honest or dishonest, and they might judge their emotions accurately or not. This means self-report EI scores could sometimes reflect a desire to give socially acceptable answers instead of showing real emotional skills. Research on this issue is mixed, some studies have found no strong link between wanting to look good and self-reported EI scores, which suggests this bias may not be as serious as it seems. It is important to keep this in mind when interpreting self-report results (Chapman,2005).

Trait EI matters for emotional wellbeing, but the relationship isn't always straightforward. If you believe you are good at understanding and managing your emotions, you might approach emotional situations with more confidence, which could help your wellbeing even if your actual skills are not strong. However, this self-belief can be inaccurate. For example, someone might think they handle emotions well but actually act in ways that are dismissive or avoidant, which are not helpful. So, just believing you are good at something does not always lead to good results. Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These abilities may influence well-being by helping people cope with difficult experiences, maintain positive emotions, manage stress, and recover from setbacks.  

* Explain trait EI.
* Distinguish trait EI from ability EI.
* Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies.
* Briefly introduce why trait EI is relevant to emotional wellbeing.

=== Defining emotional wellbeing ===
Emotional well-being theory is &lt;mark&gt;a psychological framework that explains how people experience positive emotions, evaluate their life satisfaction, and maintain a sense of purpose&lt;/mark&gt;

* '''Hedonic features:''' How a person feels in their daily moments, including joy, comfort, and a balance of positive over negative emotions.

* '''Eudaimonic features:''' Deeper reflective judgments, such as having meaning in life, pursuing personal goals, and feeling a sense of growth.
* '''The PERMA Model:''' Developed by Martin Seligman, this theory outlines five building blocks for human flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. Learn more via the PERMA Model overview. 
* Define emotional wellbeing and explain what it means in psychology.
* Explain that emotional wellbeing involves both positive and negative emotional experiences.
* Clarify that good emotional wellbeing does not mean feeling happy or positive all the time.
* Discuss the ability to recognise, understand, and manage emotions as part of healthy emotional functioning.
* Explain that experiencing emotions such as sadness, anger, anxiety, or disappointment is a normal part of emotional wellbeing.
* Discuss how emotional wellbeing may involve being able to cope with difficult emotions and recover from stressful experiences (Chen et al., 2023).
* Distinguish emotional wellbeing from the absence of mental illness or psychological distress.
* Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence.

== What is the relationship between emotional intelligence and emotional wellbeing? ==
After defining both concepts, this section examines what psychological research shows about the overall relationship between emotional intelligence and emotional wellbeing.

=== Emotional intelligence and positive wellbeing ===

* Examine whether higher emotional intelligence is associated with greater emotional wellbeing.
* Discuss research involving positive affect, happiness, life satisfaction, and subjective or psychological wellbeing.
* Explain the strength of the relationship where research allows.
* Avoid assuming that emotional intelligence directly causes greater happiness.

=== Emotional intelligence and negative emotional experiences ===

* Examine the relationship between EI and stress.
* Discuss emotional distress and negative affect.
* Consider relevant research involving anxiety or depressive symptoms.
* Explain that higher EI does not mean that someone will never experience negative emotions.
* Instead, people with stronger emotional abilities may be better able to understand and respond to difficult emotions.

=== Trait and ability emotional intelligence ===

* Compare research findings for trait and ability EI.
* Examine whether trait EI shows different relationships with wellbeing than ability EI.
* Consider how the way EI is measured could influence research findings.
* Discuss the limitations of relying heavily on self-report measures.

=== What does the evidence tell us? ===
* Bring the research together.
* Establish whether there is consistent evidence for an association between EI and emotional wellbeing.
* Distinguish correlation from causation.
* Identify any inconsistencies or limitations in the evidence.

== How does emotional intelligence influence emotional wellbeing? ==
Finding an association between emotional intelligence and wellbeing does not necessarily explain why the two are related. Several psychological processes may help explain how emotional intelligence contributes to emotional wellbeing.

'''How does emotional intelligence influence emotional wellbeing?'''  (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.)  '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing (Zomer, 2012; MacCann et al., 2022).

=== Emotional awareness and perception ===

* Explain the importance of accurately recognising emotions.
* Discuss how identifying an emotional state can help a person decide how to respond.
* Explain what may happen when people have difficulty recognising their emotions.
* Connect emotional awareness with emotional wellbeing.

=== Understanding emotions ===

* Discuss the ability to understand why an emotion has occurred.
* Explain how people can recognise changes and combinations of emotions.
* Consider how understanding the causes and consequences of emotions may support emotional functioning.
* Explain how emotional understanding may make it easier to choose an appropriate response.

=== Emotion regulation ===

* Define emotion regulation.
* Explain how EI may support the regulation of difficult emotional experiences.
* Discuss adaptive and maladaptive emotion regulation strategies.
* Consider cognitive reappraisal and suppression where relevant.
* Explain that regulating an emotion does not necessarily mean removing or suppressing it.
* Examine whether emotion regulation helps explain the relationship between EI and wellbeing.

=== Coping with stress ===

* Examine how EI may influence responses to stressful situations.
* Discuss appraisal and coping strategies.
* Consider emotional recovery and resilience.
* Connect effective coping with emotional wellbeing.

=== Social relationships and support ===

* Explain how EI may help people recognise other people's emotions.
* Discuss emotional communication.
* Examine interpersonal conflict and relationship management.
* Consider whether stronger relationships and social support provide another pathway between EI and wellbeing.

'''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.'''

Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, understanding, emotion regulation, coping with stress, and social functioning. These processes may work together rather than occurring in a simple step-by-step sequence.

== Which components of emotional intelligence are particularly important for emotional wellbeing? ==
Although emotional intelligence is often discussed as a single concept, its individual components may not contribute equally to emotional wellbeing.

(Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.)  '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019).

=== Emotion perception ===

* Examine the benefits of accurately recognising emotional states.
* Discuss the importance of identifying emotional cues in oneself and others.
* Consider limitations: recognising an emotion does not necessarily mean someone will manage it effectively.

=== Using emotions ===

* Explain what it means to use emotions to support thinking.
* Discuss how emotional information may guide attention, judgement, or problem-solving.
* Examine whether this component has a clear relationship with emotional wellbeing.

=== Emotion understanding ===

* Discuss understanding the causes and consequences of emotions.
* Consider emotional complexity and changes in emotional states.
* Examine how understanding emotions may support coping and regulation.

=== Emotion regulation and management ===

* Examine whether emotion regulation is particularly strongly related to emotional wellbeing.
* Discuss positive affect and negative affect.
* Consider emotional distress.
* Examine connections with resilience and coping.
* Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing.

=== Comparing the components ===

* Compare evidence across the different EI components.
* Consider whether any component appears particularly important for wellbeing.
* Avoid assuming that emotion regulation is the most important unless the research supports this conclusion.
* Consider whether the different abilities work together.

'''Table 2.'''

Emotional intelligence and emotional wellbeing

{| class=&quot;wikitable&quot;
!Concept
!Central concern
!Example
|-
|Emotional intelligence
|Processing, understanding and managing emotional information
|Recognising why you feel anxious and choosing an appropriate response
|-
|Emotional wellbeing
|Quality of emotional experience and functioning
|Experiencing manageable negative emotion while maintaining positive functioning
|-
|Emotion regulation
|Influencing emotional experiences or responses
|Reappraising a stressful situation rather than reacting impulsively
|}

== How can emotional intelligence be developed to support emotional wellbeing? ==
Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.)  '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing (Hodzic et al., 2018); (Nadler et al., 2020)

== Figures ==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]]
* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

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

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

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

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

==Conclusion==
* Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions.
* Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing.
* Emotion regulation, coping and interpersonal functioning may help explain this relationship.
* Different EI components and models may show different relationships with wellbeing.
* Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions.
* or universal cause of emotional wellbeing.  Return briefly to Sophie:  Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing.  
* Recommended length: 150 to 330 words

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

==See also==

* [[Emotional intelligence]]
* Emotional regulation
* [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}}
* Psychological wellbeing
* Coping
* Stress
* Positive psychology

* [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011)

* [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks)

* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

'''APA style example:'''

{{Hanging indent|1=

Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., &amp; Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x 

Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Chen, C., Kotozaki , Y., Okubo , R., &amp; Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience
. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/

Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., &amp; Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details

Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., &amp; Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613

Llamas-Díaz, D., Cabello, R., Megías-Robles, A., &amp; Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075

Luna, L. M. B., Vilar, M. M., Soto, C. M., &amp; Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696

Nadler, R., Carswell , J., &amp; Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/

Robinson, T. J., &amp; Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123

Salovey, P., &amp; Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381

MacCann, C., Double, K. S., &amp; Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819

Xu, X., Pang, W., &amp; Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details
Villanueva, L., Prado-Gascó, V., &amp; Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605

Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&amp;cbl=18750

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
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** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective]
* [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy]

{{tip|Suggestions for this section:
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__TOC__

== Overview ==
{{RoundBoxTop|theme=3}}
[[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]]

'''Scenario'''

Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict.

Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively.

Why might people respond so differently to similar emotional situations?

One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing.

Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically.

Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship.

{{RoundBoxBottom}}
* {{RoundBoxTop}}
; Focus questions
# What are emotional intelligence and emotional wellbeing? 
# What is the relationship between emotional intelligence and emotional wellbeing?
# How does emotional intelligence influence emotional wellbeing?
#Which components of emotional intelligence are particularly important for emotional wellbeing?
# How can emotional intelligence be developed to support emotional wellbeing?

{{RoundBoxBottom}}

== What are emotional intelligence and emotional wellbeing? ==
Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood.

=== Defining emotional intelligence ===
Emotional intelligence describes how people process and manage emotional information  noticing emotional cues, making sense of what they mean, and using that understanding to guide thought and behaviour (Givon et al., 2020).This is a somewhat different idea from how the term emotional is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be equated with simply being a nice person. Kindness reflects a disposition or value, whereas EI reflects an ability; a person can be highly emotionally intelligent while still setting firm boundaries or delivering difficult feedback, and a person can be warm and agreeable while struggling to accurately identify or regulate their own emotions (Salovey &amp; Grewal, 2005). Someone can therefore be outwardly calm and reserved while processing emotional information very effectively, just as someone can be outwardly expressive while struggling to understand or manage what they feel (Villanueva et al., 2020).

Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. As already noted, ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness.

These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models.

==== '''Table 1. Ability model of emotional intelligence''' ====
{| class=&quot;wikitable&quot;
!Branch
!Description
|-
|'''Perceiving emotions'''
|Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language.
|-
|'''Using emotions to facilitate thought'''
|Harnessing emotional information to guide attention, reasoning, and problem-solving.
|-
|'''Understanding emotions'''
|Comprehending emotional causes, consequences, and the way emotions change or combine over time.
|-
|'''Managing emotions'''
|Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing.
|}


Each branch can support wellbeing in its own way. Accurately noticing emotions helps people recognise what they and others feel. Using emotions to support thinking means letting feelings guide attention and judgment. Understanding emotions helps people figure out why emotions happen and how they change. Managing emotions is about handling emotional responses, which is especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend.

Explain the four branches:

# Perceiving emotions
# Using emotions to facilitate thought
# Understanding emotions[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]Managing emotions

Explain briefly how each ability could theoretically contribute to wellbeing.

&lt;quiz display=&quot;simple&quot;&gt;
Quiz 1. 
Which statement best describes emotional intelligence?
|type=&quot;()&quot;}
+ The ability to perceive, understand, use, and manage emotions.
- The ability to avoid experiencing negative emotions.
- The ability to remain happy in all situations.
- The ability to control the emotions of other people.
}
&lt;/quiz&gt;

=== Trait emotional intelligence ===
Trait EI is about how people view their own emotional abilities and tendencies, not how they perform on objective tests. Self-report EI measures reflect trait EI, much like personality tests show personality traits. Cronbach said self-report and performance-based tests differ because they measure different things: how someone usually acts compared to their best possible performance. Self-report measures show a person's typical emotional functioning, while performance-based tests try to measure their highest ability in test situations. Cronbach also mentioned that this is a useful way to see the difference, but not a complete theory. Self-report tests can still show real skills, and performance-based tests do not always capture someone's true best performance. Chapman (2005) discusses where emotional intelligence fits within personality and ability frameworks. Psychologists often use the Big Five to organise personality traits. In this view, trait EI is more like personality traits, while ability EI is like cognitive abilities. This difference explains why researchers measure them differently. Many self-report tools assess trait EI. Two common ones are the Trait Meta-Mood Scale, which measures how well someone notices, understands, and manages their moods, and the Schutte Self-Report Inventory of Emotional Intelligence, which has shown good reliability and accuracy in research.

Trait EI is measured through self-report, so it reflects how people see their own emotional intelligence. People might answer honestly or not, and they may misrepresent themselves accurately or not. This means self-report EI scores may reflect a desire to give socially acceptable answers rather than reflect real emotional skills. Research on this is mixed. Some studies have found no strong link between wanting to look good and self-reported EI scores, which suggests this bias may not be as serious as it seems. Keep this in mind when interpreting self-report results (Chapman, 2005). If you believe you are good at understanding and managing your emotions, you might approach emotional situations with more confidence, which could help your well-being even if your actual skills are not strong. However, this self-belief can be inaccurate. For example, someone might think they handle emotions well but actually act in dismissive or avoidant ways that aren't helpful. So, just believing you are good at something does not always lead to good results. Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These abilities may influence well-being by helping people cope with difficult experiences, maintain positive emotions, manage stress, and recover from setbacks.
* Explain trait EI.
* Distinguish trait EI from ability EI.
* Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies.
* Briefly introduce why trait EI is relevant to emotional wellbeing.

=== Defining emotional wellbeing ===
Emotional well-being theory is &lt;mark&gt;a psychological framework that explains how people experience positive emotions, evaluate their life satisfaction, and maintain a sense of purpose&lt;/mark&gt;

* '''Hedonic features:''' How a person feels in their daily moments, including joy, comfort, and a balance of positive over negative emotions.

* '''Eudaimonic features:''' Deeper reflective judgments, such as having meaning in life, pursuing personal goals, and feeling a sense of growth.
* '''The PERMA Model:''' Developed by Martin Seligman, this theory outlines five building blocks for human flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. Learn more via the PERMA Model overview. 
* Define emotional wellbeing and explain what it means in psychology.
* Explain that emotional wellbeing involves both positive and negative emotional experiences.
* Clarify that good emotional wellbeing does not mean feeling happy or positive all the time.
* Discuss the ability to recognise, understand, and manage emotions as part of healthy emotional functioning.
* Explain that experiencing emotions such as sadness, anger, anxiety, or disappointment is a normal part of emotional wellbeing.
* Discuss how emotional wellbeing may involve being able to cope with difficult emotions and recover from stressful experiences (Chen et al., 2023).
* Distinguish emotional wellbeing from the absence of mental illness or psychological distress.
* Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence.

== What is the relationship between emotional intelligence and emotional wellbeing? ==
After defining both concepts, this section examines what psychological research shows about the overall relationship between emotional intelligence and emotional wellbeing.

=== Emotional intelligence and positive wellbeing ===

* Examine whether higher emotional intelligence is associated with greater emotional wellbeing.
* Discuss research involving positive affect, happiness, life satisfaction, and subjective or psychological wellbeing.
* Explain the strength of the relationship where research allows.
* Avoid assuming that emotional intelligence directly causes greater happiness.

=== Emotional intelligence and negative emotional experiences ===

* Examine the relationship between EI and stress.
* Discuss emotional distress and negative affect.
* Consider relevant research involving anxiety or depressive symptoms.
* Explain that higher EI does not mean that someone will never experience negative emotions.
* Instead, people with stronger emotional abilities may be better able to understand and respond to difficult emotions.

=== Trait and ability emotional intelligence ===

* Compare research findings for trait and ability EI.
* Examine whether trait EI shows different relationships with wellbeing than ability EI.
* Consider how the way EI is measured could influence research findings.
* Discuss the limitations of relying heavily on self-report measures.

=== What does the evidence tell us? ===
* Bring the research together.
* Establish whether there is consistent evidence for an association between EI and emotional wellbeing.
* Distinguish correlation from causation.
* Identify any inconsistencies or limitations in the evidence.

== How does emotional intelligence influence emotional wellbeing? ==
Finding an association between emotional intelligence and wellbeing does not necessarily explain why the two are related. Several psychological processes may help explain how emotional intelligence contributes to emotional wellbeing.

'''How does emotional intelligence influence emotional wellbeing?'''  (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.)  '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing (Zomer, 2012; MacCann et al., 2022).

=== Emotional awareness and perception ===

* Explain the importance of accurately recognising emotions.
* Discuss how identifying an emotional state can help a person decide how to respond.
* Explain what may happen when people have difficulty recognising their emotions.
* Connect emotional awareness with emotional wellbeing.

=== Understanding emotions ===

* Discuss the ability to understand why an emotion has occurred.
* Explain how people can recognise changes and combinations of emotions.
* Consider how understanding the causes and consequences of emotions may support emotional functioning.
* Explain how emotional understanding may make it easier to choose an appropriate response.

=== Emotion regulation ===

* Define emotion regulation.
* Explain how EI may support the regulation of difficult emotional experiences.
* Discuss adaptive and maladaptive emotion regulation strategies.
* Consider cognitive reappraisal and suppression where relevant.
* Explain that regulating an emotion does not necessarily mean removing or suppressing it.
* Examine whether emotion regulation helps explain the relationship between EI and wellbeing.

=== Coping with stress ===

* Examine how EI may influence responses to stressful situations.
* Discuss appraisal and coping strategies.
* Consider emotional recovery and resilience.
* Connect effective coping with emotional wellbeing.

=== Social relationships and support ===

* Explain how EI may help people recognise other people's emotions.
* Discuss emotional communication.
* Examine interpersonal conflict and relationship management.
* Consider whether stronger relationships and social support provide another pathway between EI and wellbeing.

'''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.'''

Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, understanding, emotion regulation, coping with stress, and social functioning. These processes may work together rather than occurring in a simple step-by-step sequence.

== Which components of emotional intelligence are particularly important for emotional wellbeing? ==
Although emotional intelligence is often discussed as a single concept, its individual components may not contribute equally to emotional wellbeing.

(Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.)  '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019).

=== Emotion perception ===

* Examine the benefits of accurately recognising emotional states.
* Discuss the importance of identifying emotional cues in oneself and others.
* Consider limitations: recognising an emotion does not necessarily mean someone will manage it effectively.

=== Using emotions ===

* Explain what it means to use emotions to support thinking.
* Discuss how emotional information may guide attention, judgement, or problem-solving.
* Examine whether this component has a clear relationship with emotional wellbeing.

=== Emotion understanding ===

* Discuss understanding the causes and consequences of emotions.
* Consider emotional complexity and changes in emotional states.
* Examine how understanding emotions may support coping and regulation.

=== Emotion regulation and management ===

* Examine whether emotion regulation is particularly strongly related to emotional wellbeing.
* Discuss positive affect and negative affect.
* Consider emotional distress.
* Examine connections with resilience and coping.
* Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing.

=== Comparing the components ===

* Compare evidence across the different EI components.
* Consider whether any component appears particularly important for wellbeing.
* Avoid assuming that emotion regulation is the most important unless the research supports this conclusion.
* Consider whether the different abilities work together.

'''Table 2.'''

Emotional intelligence and emotional wellbeing

{| class=&quot;wikitable&quot;
!Concept
!Central concern
!Example
|-
|Emotional intelligence
|Processing, understanding and managing emotional information
|Recognising why you feel anxious and choosing an appropriate response
|-
|Emotional wellbeing
|Quality of emotional experience and functioning
|Experiencing manageable negative emotion while maintaining positive functioning
|-
|Emotion regulation
|Influencing emotional experiences or responses
|Reappraising a stressful situation rather than reacting impulsively
|}

== How can emotional intelligence be developed to support emotional wellbeing? ==
Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.)  '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing (Hodzic et al., 2018); (Nadler et al., 2020)

== Figures ==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]]
* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

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

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

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

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

==Conclusion==
* Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions.
* Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing.
* Emotion regulation, coping and interpersonal functioning may help explain this relationship.
* Different EI components and models may show different relationships with wellbeing.
* Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions.
* or universal cause of emotional wellbeing.  Return briefly to Sophie:  Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing.  
* Recommended length: 150 to 330 words

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

==See also==

* [[Emotional intelligence]]
* Emotional regulation
* [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}}
* Psychological wellbeing
* Coping
* Stress
* Positive psychology

* [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011)

* [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks)

* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

'''APA style example:'''

{{Hanging indent|1=

Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., &amp; Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x 

Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Chen, C., Kotozaki , Y., Okubo , R., &amp; Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience
. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/

Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., &amp; Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details

Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., &amp; Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613

Llamas-Díaz, D., Cabello, R., Megías-Robles, A., &amp; Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075

Luna, L. M. B., Vilar, M. M., Soto, C. M., &amp; Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696

Nadler, R., Carswell , J., &amp; Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/

Robinson, T. J., &amp; Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123

Salovey, P., &amp; Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381

MacCann, C., Double, K. S., &amp; Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819

Xu, X., Pang, W., &amp; Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details
Villanueva, L., Prado-Gascó, V., &amp; Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605

Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&amp;cbl=18750

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
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* The most common mistakes include:
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** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective]
* [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy]

{{tip|Suggestions for this section:
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__TOC__

== Overview ==
{{RoundBoxTop|theme=3}}
[[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]]

'''Scenario'''

Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict.

Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively.

Why might people respond so differently to similar emotional situations?

One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing.

Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically.

Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship.

{{RoundBoxBottom}}
* {{RoundBoxTop}}
; Focus questions
# What are emotional intelligence and emotional wellbeing? 
# What is the relationship between emotional intelligence and emotional wellbeing?
# How does emotional intelligence influence emotional wellbeing?
#Which components of emotional intelligence are particularly important for emotional wellbeing?
# How can emotional intelligence be developed to support emotional wellbeing?

{{RoundBoxBottom}}

== What are emotional intelligence and emotional wellbeing? ==
Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood.

=== Defining emotional intelligence ===
Emotional intelligence describes how people process and manage emotional information  noticing emotional cues, making sense of what they mean, and using that understanding to guide thought and behaviour (Givon et al., 2020).This is a somewhat different idea from how the term emotional is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be equated with simply being a nice person. Kindness reflects a disposition or value, whereas EI reflects an ability; a person can be highly emotionally intelligent while still setting firm boundaries or delivering difficult feedback, and a person can be warm and agreeable while struggling to accurately identify or regulate their own emotions (Salovey &amp; Grewal, 2005). Someone can therefore be outwardly calm and reserved while processing emotional information very effectively, just as someone can be outwardly expressive while struggling to understand or manage what they feel (Villanueva et al., 2020).

Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. As already noted, ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness.

These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models.

==== '''Table 1. Ability model of emotional intelligence''' ====
{| class=&quot;wikitable&quot;
!Branch
!Description
|-
|'''Perceiving emotions'''
|Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language.
|-
|'''Using emotions to facilitate thought'''
|Harnessing emotional information to guide attention, reasoning, and problem-solving.
|-
|'''Understanding emotions'''
|Comprehending emotional causes, consequences, and the way emotions change or combine over time.
|-
|'''Managing emotions'''
|Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing.
|}


Each branch can support wellbeing in its own way. Accurately noticing emotions helps people recognise what they and others feel. Using emotions to support thinking means letting feelings guide attention and judgment. Understanding emotions helps people figure out why emotions happen and how they change. Managing emotions is about handling emotional responses, which is especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend.

Explain the four branches:

# Perceiving emotions
# Using emotions to facilitate thought
# Understanding emotions[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]Managing emotions

Explain briefly how each ability could theoretically contribute to wellbeing.

&lt;quiz display=&quot;simple&quot;&gt;
Quiz 1. 
Which statement best describes emotional intelligence?
|type=&quot;()&quot;}
+ The ability to perceive, understand, use, and manage emotions.
- The ability to avoid experiencing negative emotions.
- The ability to remain happy in all situations.
- The ability to control the emotions of other people.
}
&lt;/quiz&gt;

=== Trait emotional intelligence ===
Trait EI is about how people view their own emotional abilities and tendencies, not how they perform on objective tests. Self-report EI measures reflect trait EI, much like personality tests show personality traits. Cronbach said self-report and performance-based tests differ because they measure different things: how someone usually acts compared to their best possible performance. Self-report measures show a person's typical emotional functioning, while performance-based tests try to measure their highest ability in test situations. Cronbach also mentioned that this is a useful way to see the difference, but not a complete theory. Self-report tests can still show real skills, and performance-based tests do not always capture someone's true best performance. Chapman (2005) discusses where emotional intelligence fits within personality and ability frameworks. Psychologists often use the Big Five to organise personality traits. In this view, trait EI is more like personality traits, while ability EI is like cognitive abilities. This difference explains why researchers measure them differently. Many self-report tools assess trait EI. Two common ones are the Trait Meta-Mood Scale, which measures how well someone notices, understands, and manages their moods, and the Schutte Self-Report Inventory of Emotional Intelligence, which has shown good reliability and accuracy in research.

Trait EI is measured through self-report, so it reflects how people see their own emotional intelligence. People might answer honestly or not, and they may misrepresent themselves accurately or not. This means self-report EI scores may reflect a desire to give socially acceptable answers rather than reflect real emotional skills. Research on this is mixed. Some studies have found no strong link between wanting to look good and self-reported EI scores, which suggests this bias may not be as serious as it seems. Keep this in mind when interpreting self-report results (Chapman, 2005). If you believe you are good at understanding and managing your emotions, you might approach emotional situations with more confidence, which could help your well-being even if your actual skills are not strong. However, this self-belief can be inaccurate. For example, someone might think they handle emotions well but actually act in dismissive or avoidant ways that aren't helpful. So, just believing you are good at something does not always lead to good results. Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These abilities may influence well-being by helping people cope with difficult experiences, maintain positive emotions, manage stress, and recover from setbacks.
* Explain trait EI.
* Distinguish trait EI from ability EI.
* Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies.
* Briefly introduce why trait EI is relevant to emotional wellbeing.

=== Defining emotional wellbeing ===
Emotional well-being theory is &lt;mark&gt;a psychological framework that explains how people experience positive emotions, evaluate their life satisfaction, and maintain a sense of purpose&lt;/mark&gt;

* '''Hedonic features:''' How a person feels in their daily moments, including joy, comfort, and a balance of positive over negative emotions.

* '''Eudaimonic features:''' Deeper reflective judgments, such as having meaning in life, pursuing personal goals, and feeling a sense of growth.
* '''The PERMA Model:''' Developed by Martin Seligman, this theory outlines five building blocks for human flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. Learn more via the PERMA Model overview. 
* Define emotional wellbeing and explain what it means in psychology.
* Explain that emotional wellbeing involves both positive and negative emotional experiences.
* Clarify that good emotional wellbeing does not mean feeling happy or positive all the time.
* Discuss the ability to recognise, understand, and manage emotions as part of healthy emotional functioning.
* Explain that experiencing emotions such as sadness, anger, anxiety, or disappointment is a normal part of emotional wellbeing.
* Discuss how emotional wellbeing may involve being able to cope with difficult emotions and recover from stressful experiences (Chen et al., 2023).
* Distinguish emotional wellbeing from the absence of mental illness or psychological distress.
* Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence.

== What is the relationship between emotional intelligence and emotional wellbeing? ==
After defining both concepts, this section examines what psychological research shows about the overall relationship between emotional intelligence and emotional wellbeing.

=== Emotional intelligence and positive wellbeing ===

* Examine whether higher emotional intelligence is associated with greater emotional wellbeing.
* Discuss research involving positive affect, happiness, life satisfaction, and subjective or psychological wellbeing.
* Explain the strength of the relationship where research allows.
* Avoid assuming that emotional intelligence directly causes greater happiness.

=== Emotional intelligence and negative emotional experiences ===

* Examine the relationship between EI and stress.
* Discuss emotional distress and negative affect.
* Consider relevant research involving anxiety or depressive symptoms.
* Explain that higher EI does not mean that someone will never experience negative emotions.
* Instead, people with stronger emotional abilities may be better able to understand and respond to difficult emotions.

=== Trait and ability emotional intelligence ===

* Compare research findings for trait and ability EI.
* Examine whether trait EI shows different relationships with wellbeing than ability EI.
* Consider how the way EI is measured could influence research findings.
* Discuss the limitations of relying heavily on self-report measures.

=== What does the evidence tell us? ===
* Bring the research together.
* Establish whether there is consistent evidence for an association between EI and emotional wellbeing.
* Distinguish correlation from causation.
* Identify any inconsistencies or limitations in the evidence.

Finding an association between emotional intelligence and wellbeing does not necessarily explain why the two are related. Several psychological processes may help explain how emotional intelligence contributes to emotional wellbeing.

'''How does emotional intelligence influence emotional wellbeing?'''  (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.)  '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing (Zomer, 2012; MacCann et al., 2022).

=== Emotional awareness and perception ===

* Explain the importance of accurately recognising emotions.
* Discuss how identifying an emotional state can help a person decide how to respond.
* Explain what may happen when people have difficulty recognising their emotions.
* Connect emotional awareness with emotional wellbeing.

=== Understanding emotions ===

* Discuss the ability to understand why an emotion has occurred.
* Explain how people can recognise changes and combinations of emotions.
* Consider how understanding the causes and consequences of emotions may support emotional functioning.
* Explain how emotional understanding may make it easier to choose an appropriate response.

=== Emotion regulation ===

* Define emotion regulation.
* Explain how EI may support the regulation of difficult emotional experiences.
* Discuss adaptive and maladaptive emotion regulation strategies.
* Consider cognitive reappraisal and suppression where relevant.
* Explain that regulating an emotion does not necessarily mean removing or suppressing it.
* Examine whether emotion regulation helps explain the relationship between EI and wellbeing.

=== Coping with stress ===

* Examine how EI may influence responses to stressful situations.
* Discuss appraisal and coping strategies.
* Consider emotional recovery and resilience.
* Connect effective coping with emotional wellbeing.

=== Social relationships and support ===

* Explain how EI may help people recognise other people's emotions.
* Discuss emotional communication.
* Examine interpersonal conflict and relationship management.
* Consider whether stronger relationships and social support provide another pathway between EI and wellbeing.

'''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.'''

Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, understanding, emotion regulation, coping with stress, and social functioning. These processes may work together rather than occurring in a simple step-by-step sequence.

== Which components of emotional intelligence are particularly important for emotional wellbeing? ==
Although emotional intelligence is often discussed as a single concept, its individual components may not contribute equally to emotional wellbeing.

(Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.)  '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019).

=== Emotion perception ===

* Examine the benefits of accurately recognising emotional states.
* Discuss the importance of identifying emotional cues in oneself and others.
* Consider limitations: recognising an emotion does not necessarily mean someone will manage it effectively.

=== Using emotions ===

* Explain what it means to use emotions to support thinking.
* Discuss how emotional information may guide attention, judgement, or problem-solving.
* Examine whether this component has a clear relationship with emotional wellbeing.

=== Emotion understanding ===

* Discuss understanding the causes and consequences of emotions.
* Consider emotional complexity and changes in emotional states.
* Examine how understanding emotions may support coping and regulation.

=== Emotion regulation and management ===

* Examine whether emotion regulation is particularly strongly related to emotional wellbeing.
* Discuss positive affect and negative affect.
* Consider emotional distress.
* Examine connections with resilience and coping.
* Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing.

=== Comparing the components ===

* Compare evidence across the different EI components.
* Consider whether any component appears particularly important for wellbeing.
* Avoid assuming that emotion regulation is the most important unless the research supports this conclusion.
* Consider whether the different abilities work together.

'''Table 2.'''

Emotional intelligence and emotional wellbeing

{| class=&quot;wikitable&quot;
!Concept
!Central concern
!Example
|-
|Emotional intelligence
|Processing, understanding and managing emotional information
|Recognising why you feel anxious and choosing an appropriate response
|-
|Emotional wellbeing
|Quality of emotional experience and functioning
|Experiencing manageable negative emotion while maintaining positive functioning
|-
|Emotion regulation
|Influencing emotional experiences or responses
|Reappraising a stressful situation rather than reacting impulsively
|}

== How can emotional intelligence be developed to support emotional wellbeing? ==
Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.)  '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing (Hodzic et al., 2018); (Nadler et al., 2020)

== Figures ==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]]
* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

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

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

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

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

==Conclusion==
* Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions.
* Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing.
* Emotion regulation, coping and interpersonal functioning may help explain this relationship.
* Different EI components and models may show different relationships with wellbeing.
* Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions.
* or universal cause of emotional wellbeing.  Return briefly to Sophie:  Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing.  
* Recommended length: 150 to 330 words

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

==See also==

* [[Emotional intelligence]]
* Emotional regulation
* [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}}
* Psychological wellbeing
* Coping
* Stress
* Positive psychology

* [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011)

* [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks)

* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

'''APA style example:'''

{{Hanging indent|1=

Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., &amp; Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x 

Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Chen, C., Kotozaki , Y., Okubo , R., &amp; Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience
. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/

Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., &amp; Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details

Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., &amp; Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613

Llamas-Díaz, D., Cabello, R., Megías-Robles, A., &amp; Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075

Luna, L. M. B., Vilar, M. M., Soto, C. M., &amp; Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696

Nadler, R., Carswell , J., &amp; Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/

Robinson, T. J., &amp; Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123

Salovey, P., &amp; Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381

MacCann, C., Double, K. S., &amp; Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819

Xu, X., Pang, W., &amp; Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details
Villanueva, L., Prado-Gascó, V., &amp; Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605

Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&amp;cbl=18750

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
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** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective]
* [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
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__TOC__

== Overview ==
{{RoundBoxTop|theme=3}}
[[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]]

'''Scenario'''

Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict.

Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively.

Why might people respond so differently to similar emotional situations?

One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing.

Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically.

Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship.

{{RoundBoxBottom}}
* {{RoundBoxTop}}
; Focus questions
# What are emotional intelligence and emotional wellbeing? 
# What is the relationship between emotional intelligence and emotional wellbeing?
#Which components of emotional intelligence are particularly important for emotional wellbeing?
# How can emotional intelligence be developed to support emotional wellbeing?

{{RoundBoxBottom}}

== What are emotional intelligence and emotional wellbeing? ==
Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood.

=== Defining emotional intelligence ===
Emotional intelligence describes how people process and manage emotional information  noticing emotional cues, making sense of what they mean, and using that understanding to guide thought and behaviour (Givon et al., 2020).This is a somewhat different idea from how the term emotional is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be equated with simply being a nice person. Kindness reflects a disposition or value, whereas EI reflects an ability; a person can be highly emotionally intelligent while still setting firm boundaries or delivering difficult feedback, and a person can be warm and agreeable while struggling to accurately identify or regulate their own emotions (Salovey &amp; Grewal, 2005). Someone can therefore be outwardly calm and reserved while processing emotional information very effectively, just as someone can be outwardly expressive while struggling to understand or manage what they feel (Villanueva et al., 2020).

Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. As already noted, ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness.

These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models.

==== '''Table 1. Ability model of emotional intelligence''' ====
{| class=&quot;wikitable&quot;
!Branch
!Description
|-
|'''Perceiving emotions'''
|Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language.
|-
|'''Using emotions to facilitate thought'''
|Harnessing emotional information to guide attention, reasoning, and problem-solving.
|-
|'''Understanding emotions'''
|Comprehending emotional causes, consequences, and the way emotions change or combine over time.
|-
|'''Managing emotions'''
|Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing.
|}


Each branch can support wellbeing in its own way. Accurately noticing emotions helps people recognise what they and others feel. Using emotions to support thinking means letting feelings guide attention and judgment. Understanding emotions helps people figure out why emotions happen and how they change. Managing emotions is about handling emotional responses, which is especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend.

Explain the four branches:

# Perceiving emotions
# Using emotions to facilitate thought
# Understanding emotions[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]Managing emotions

Explain briefly how each ability could theoretically contribute to wellbeing.

&lt;quiz display=&quot;simple&quot;&gt;
Quiz 1. 
Which statement best describes emotional intelligence?
|type=&quot;()&quot;}
+ The ability to perceive, understand, use, and manage emotions.
- The ability to avoid experiencing negative emotions.
- The ability to remain happy in all situations.
- The ability to control the emotions of other people.
}
&lt;/quiz&gt;

=== Trait emotional intelligence ===
Trait EI is about how people view their own emotional abilities and tendencies, not how they perform on objective tests. Self-report EI measures reflect trait EI, much like personality tests show personality traits. Cronbach said self-report and performance-based tests differ because they measure different things: how someone usually acts compared to their best possible performance. Self-report measures show a person's typical emotional functioning, while performance-based tests try to measure their highest ability in test situations. Cronbach also mentioned that this is a useful way to see the difference, but not a complete theory. Self-report tests can still show real skills, and performance-based tests do not always capture someone's true best performance. Chapman (2005) discusses where emotional intelligence fits within personality and ability frameworks. Psychologists often use the Big Five to organise personality traits. In this view, trait EI is more like personality traits, while ability EI is like cognitive abilities. This difference explains why researchers measure them differently. Many self-report tools assess trait EI. Two common ones are the Trait Meta-Mood Scale, which measures how well someone notices, understands, and manages their moods, and the Schutte Self-Report Inventory of Emotional Intelligence, which has shown good reliability and accuracy in research.

Trait EI is measured through self-report, so it reflects how people see their own emotional intelligence. People might answer honestly or not, and they may misrepresent themselves accurately or not. This means self-report EI scores may reflect a desire to give socially acceptable answers rather than reflect real emotional skills. Research on this is mixed. Some studies have found no strong link between wanting to look good and self-reported EI scores, which suggests this bias may not be as serious as it seems. Keep this in mind when interpreting self-report results (Chapman, 2005). If you believe you are good at understanding and managing your emotions, you might approach emotional situations with more confidence, which could help your well-being even if your actual skills are not strong. However, this self-belief can be inaccurate. For example, someone might think they handle emotions well but actually act in dismissive or avoidant ways that aren't helpful. So, just believing you are good at something does not always lead to good results. Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These abilities may influence well-being by helping people cope with difficult experiences, maintain positive emotions, manage stress, and recover from setbacks.
* Explain trait EI.
* Distinguish trait EI from ability EI.
* Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies.
* Briefly introduce why trait EI is relevant to emotional wellbeing.

=== Defining emotional wellbeing ===
Emotional well-being theory is &lt;mark&gt;a psychological framework that explains how people experience positive emotions, evaluate their life satisfaction, and maintain a sense of purpose&lt;/mark&gt;

* '''Hedonic features:''' How a person feels in their daily moments, including joy, comfort, and a balance of positive over negative emotions.

* '''Eudaimonic features:''' Deeper reflective judgments, such as having meaning in life, pursuing personal goals, and feeling a sense of growth.
* '''The PERMA Model:''' Developed by Martin Seligman, this theory outlines five building blocks for human flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. Learn more via the PERMA Model overview. 
* Define emotional wellbeing and explain what it means in psychology.
* Explain that emotional wellbeing involves both positive and negative emotional experiences.
* Clarify that good emotional wellbeing does not mean feeling happy or positive all the time.
* Discuss the ability to recognise, understand, and manage emotions as part of healthy emotional functioning.
* Explain that experiencing emotions such as sadness, anger, anxiety, or disappointment is a normal part of emotional wellbeing.
* Discuss how emotional wellbeing may involve being able to cope with difficult emotions and recover from stressful experiences (Chen et al., 2023).
* Distinguish emotional wellbeing from the absence of mental illness or psychological distress.
* Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence.

== What is the relationship between emotional intelligence and emotional wellbeing? ==
After defining both concepts, this section examines what psychological research shows about the overall relationship between emotional intelligence and emotional wellbeing.

=== Emotional intelligence and positive wellbeing ===

* Examine whether higher emotional intelligence is associated with greater emotional wellbeing.
* Discuss research involving positive affect, happiness, life satisfaction, and subjective or psychological wellbeing.
* Explain the strength of the relationship where research allows.
* Avoid assuming that emotional intelligence directly causes greater happiness.

=== Emotional intelligence and negative emotional experiences ===

* Examine the relationship between EI and stress.
* Discuss emotional distress and negative affect.
* Consider relevant research involving anxiety or depressive symptoms.
* Explain that higher EI does not mean that someone will never experience negative emotions.
* Instead, people with stronger emotional abilities may be better able to understand and respond to difficult emotions.

=== Trait and ability emotional intelligence ===

* Compare research findings for trait and ability EI.
* Examine whether trait EI shows different relationships with wellbeing than ability EI.
* Consider how the way EI is measured could influence research findings.
* Discuss the limitations of relying heavily on self-report measures.

=== What does the evidence tell us? ===
* Bring the research together.
* Establish whether there is consistent evidence for an association between EI and emotional wellbeing.
* Distinguish correlation from causation.
* Identify any inconsistencies or limitations in the evidence.

Finding an association between emotional intelligence and wellbeing does not necessarily explain why the two are related. Several psychological processes may help explain how emotional intelligence contributes to emotional wellbeing.

'''How does emotional intelligence influence emotional wellbeing?'''  (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.)  '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing (Zomer, 2012; MacCann et al., 2022).

=== Emotional awareness and perception ===

* Explain the importance of accurately recognising emotions.
* Discuss how identifying an emotional state can help a person decide how to respond.
* Explain what may happen when people have difficulty recognising their emotions.
* Connect emotional awareness with emotional wellbeing.

=== Understanding emotions ===

* Discuss the ability to understand why an emotion has occurred.
* Explain how people can recognise changes and combinations of emotions.
* Consider how understanding the causes and consequences of emotions may support emotional functioning.
* Explain how emotional understanding may make it easier to choose an appropriate response.

=== Emotion regulation ===

* Define emotion regulation.
* Explain how EI may support the regulation of difficult emotional experiences.
* Discuss adaptive and maladaptive emotion regulation strategies.
* Consider cognitive reappraisal and suppression where relevant.
* Explain that regulating an emotion does not necessarily mean removing or suppressing it.
* Examine whether emotion regulation helps explain the relationship between EI and wellbeing.

=== Coping with stress ===

* Examine how EI may influence responses to stressful situations.
* Discuss appraisal and coping strategies.
* Consider emotional recovery and resilience.
* Connect effective coping with emotional wellbeing.

=== Social relationships and support ===

* Explain how EI may help people recognise other people's emotions.
* Discuss emotional communication.
* Examine interpersonal conflict and relationship management.
* Consider whether stronger relationships and social support provide another pathway between EI and wellbeing.

'''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.'''

Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, understanding, emotion regulation, coping with stress, and social functioning. These processes may work together rather than occurring in a simple step-by-step sequence.

== Which components of emotional intelligence are particularly important for emotional wellbeing? ==
Although emotional intelligence is often discussed as a single concept, its individual components may not contribute equally to emotional wellbeing.

(Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.)  '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019).

=== Emotion perception ===

* Examine the benefits of accurately recognising emotional states.
* Discuss the importance of identifying emotional cues in oneself and others.
* Consider limitations: recognising an emotion does not necessarily mean someone will manage it effectively.

=== Using emotions ===

* Explain what it means to use emotions to support thinking.
* Discuss how emotional information may guide attention, judgement, or problem-solving.
* Examine whether this component has a clear relationship with emotional wellbeing.

=== Emotion understanding ===

* Discuss understanding the causes and consequences of emotions.
* Consider emotional complexity and changes in emotional states.
* Examine how understanding emotions may support coping and regulation.

=== Emotion regulation and management ===

* Examine whether emotion regulation is particularly strongly related to emotional wellbeing.
* Discuss positive affect and negative affect.
* Consider emotional distress.
* Examine connections with resilience and coping.
* Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing.

=== Comparing the components ===

* Compare evidence across the different EI components.
* Consider whether any component appears particularly important for wellbeing.
* Avoid assuming that emotion regulation is the most important unless the research supports this conclusion.
* Consider whether the different abilities work together.

'''Table 2.'''

Emotional intelligence and emotional wellbeing

{| class=&quot;wikitable&quot;
!Concept
!Central concern
!Example
|-
|Emotional intelligence
|Processing, understanding and managing emotional information
|Recognising why you feel anxious and choosing an appropriate response
|-
|Emotional wellbeing
|Quality of emotional experience and functioning
|Experiencing manageable negative emotion while maintaining positive functioning
|-
|Emotion regulation
|Influencing emotional experiences or responses
|Reappraising a stressful situation rather than reacting impulsively
|}

== How can emotional intelligence be developed to support emotional wellbeing? ==
Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.)  '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing (Hodzic et al., 2018); (Nadler et al., 2020)

== Figures ==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]]
* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

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

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

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

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

==Conclusion==
* Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions.
* Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing.
* Emotion regulation, coping and interpersonal functioning may help explain this relationship.
* Different EI components and models may show different relationships with wellbeing.
* Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions.
* or universal cause of emotional wellbeing.  Return briefly to Sophie:  Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing.  
* Recommended length: 150 to 330 words

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

==See also==

* [[Emotional intelligence]]
* Emotional regulation
* [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}}
* Psychological wellbeing
* Coping
* Stress
* Positive psychology

* [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011)

* [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks)

* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

'''APA style example:'''

{{Hanging indent|1=

Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., &amp; Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x 

Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&amp;sourcetype=Dissertations%20&amp;%20Theses

Chen, C., Kotozaki , Y., Okubo , R., &amp; Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience
. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/

Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., &amp; Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details

Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., &amp; Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613

Llamas-Díaz, D., Cabello, R., Megías-Robles, A., &amp; Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075

Luna, L. M. B., Vilar, M. M., Soto, C. M., &amp; Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696

Nadler, R., Carswell , J., &amp; Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/

Robinson, T. J., &amp; Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123

Salovey, P., &amp; Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381

MacCann, C., Double, K. S., &amp; Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819

Xu, X., Pang, W., &amp; Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details
Villanueva, L., Prado-Gascó, V., &amp; Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605

Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&amp;cbl=18750

}}

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

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective]
* [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__

==Overview==
{{RoundBoxTop|theme=6}}
[[File:School level test of Wikischolar 2026 at Ispahani Public School &amp; College 08.jpg|thumb|'''Figure 1'''. Stressful exam {{ic|Consider expanding this figure caption to make the connection to the scenario more clear}}]]

''' Case Study - Exam stressors'''

Michael is halfway through a university exam, in a small classroom filled with 30 other examinees. Suddenly, he realises that he misread a question and wasted the past 15 minutes. His heat{{sp}} rate spikes, thoughts start racing and {{missing}} begins to panic. Becoming overwhelmed at the sudden onset of negativity, he felt{{g}} the urge to give up.

Normally, Michael copes with [[W: Psychological stress | stress]] and [[anxiety]] through exercise as he finds this is the most consistent modulator for his emotions. But in an exam room, this strategy becomes moot.

Michael stops, realises that the current negativity isn't helping his situation, and identifies that panic is only hindering his performance and that emotional regulation is needed if he wants to do well. He starts to tell himself &quot;I can still get partial marks for that question&quot;. Realising that the positive self-talk is helping he continues &quot;On this next question I'll make sure to focus on all facet's{{g}} of what the question asks&quot;. By the end of the next question Michael once again felt a sense of confidence in his ability to pass the exam.
{{RoundBoxBottom}}

Emotion regulation refers to the processes through which individuals monitor, evaluate and modify their emotional responses {{ic|APA style uses serial commas}}. Contemporary psychological science emphasises that regulation is not a singular act but a dynamic, context-sensitive system continuously unfolding over time (Bonanno &amp; Burton, 2013). Gross's (2015) Extended Process Model (EPM) captures this complexity by organising regulation into three iterative stages: identification, selection and implementation. Each governed by a higher-order valuation system that determines whether, when, and how emotions should be regulated. This framework highlights that regulatory success depends not only on the strategy chosen but on the fit between regulatory goals, contextual affordances, and the individual's cognitive resources.

Emotional regulation is central to mental health. [[Motivation and emotion/Book/2026/Emotion dysregulation|Emotional dysregulation]] predicts a wide range of difficulties, including the strong associated between dysregulation and anxiety in autistic youth (Connor et al., 2020). Meta-analytic evidence further demonstrates that habitual reappraisal is linked to better wellbeing, whereas suppression is often linked to poorer outcomes, though these patterns seem to vary across contexts (Chen et al., 2025). These findings underscore the need to understand ''why'' emotional regulation works differently across individuals and situations.

{{RoundBoxTop|theme=6}}
'''Focus questions'''

* How do cultural [[W: social norms | norms]] shape the valuation of regulatory goals within the EPM?
* What role does [[W: cognitive flexibility | cognitive flexibility]] play in the EPM’s ability to explain individual differences in regulatory effectiveness?
* How does the EPM explain the strong predictive link between [[Motivation and emotion/Book/2026/Emotion dysregulation | emotional dysregulation]] and anxiety in autistic youth?
* In what types of situations does switching to distraction improve regulatory outcomes, and why might switching to [[W: cognitive appraisal |reappraisal ]] impair them?

{{RoundBoxBottom}}

== The Extended Process Model of Emotional Regulation ==

* Emotion regulation as a higher‑order valuation system modifying first‑order emotional responses (Gross, 2015).
* Three‑stage regulatory cycle: '''identification''', '''selection''', '''implementation''' (Gross, 2015).
** Identification: The identification stage concerns the fundamental question of whether emotion regulation is required at all. According to Gross (2015), this stage is governed by a higher-order valuation system (explain this and then edit the dot points above) that evaluates the unfolding emotional response against current goals, contextual affordances, and motivational priorities. Identification involves detecting discrepancies between desired and actual emotional states. Essentially, recognising that the current, experienced emotion is misaligned with what the situation demands. This is an evaluative process, integrating prior learning, cultural norms and situational constraints to determine the necessity of regulation. Failure at this stage, such as misidentifying an emotion as irrelevant or failing to recognise a maladaptive trajectory can derailed the entire regulatory cycle. Thus, the identification stage acts as the gatekeeper of emotional regulation, ensuring cognitive resources are deployed only when emotional change is instrumentally valuable.
** Selection: Once regulation is deemed necessary, the selection stage determines what strategy should be used. Gross (2015) emphasises that this stage involves choosing among diverse regulatory families, such as attentional deployment, cognitive change, or response modulation, based on their anticipated fit with situational demands. Selection is a predictive process; the valuation system simulates the likely consequences of each strategy, weighing cognitive costs, contextual differences in regulatory repertoire (Bonanno &amp; Burton, 2013), meaning that people with broader, more flexible strategy selection requires both contextual sensitivity and strategic foresight; poor selection may lead to strategies that are cognitively overtaxing, situationally inappropriate, or counterproductive. In this way, selection acts as the model's optimisation mechanism, aligning regulatory tactics with the dynamic structure of the emotional episode.
** Implementation: Implementation concerns ''how'' the chosen strategy is enacted in real time. Gross (2015) describes this stage as the translation of abstract regulatory intentions into concrete tactics, such as shifting attention, reframing meaning or modulating expressive behavior. Implementation is effortful and dynamic; it unfolds over time, requiring sustained cognitive control and continuous adjustment as the emotional episode evolves. Crucially, implementation is not a single action but an iterative process in which the tactic is maintained, intensified, or abandoned depending on its moment-to-moment effectiveness. Research has shown that ineffective implementation predicts strategy switching (Adamczyk et al., 20204), highlighting that implementation is tightly coupled with feedback processes. Thus, implementation is the engine of regulation, where theoretical  strategies become emboied actions that shape the emotional trajectory.
* Emphasis on temporal dynamics, regulation unfolds iteratively and adjusts based on feedback. - Maintenance
* Situated cognition: regulatory success depends on contextual affordances, not inherent strategy value (Gross, 2015).
* Sets the foundation for exploring cultural norms, cognitive flexibility, developmental trajectories, and strategy effectiveness.

&lt;quiz display=&quot;simple&quot;&gt;
{Which of these is not a stage in the regulatory cycle?|type =&quot;()&quot;}

+ Yelling 
- Identification
- Selection
- Implementation

{According to EPM, After Selecting One Strategy to Use, Emotional Regulation is Done: {{ic|Use sentence casing}}}

- True
+ False

{Improvements will be made to this quiz}

+ True
- False
&lt;/quiz&gt;

==The Effects of Culture on Emotional Regulation==

* Cultural norms shape valuation systems that determine regulatory goals and strategy desirability (Chen et al., 2025).
* Reappraisal linked to better mental health across cultures, but strength of association varies with cultural dimensions such as uncertainty avoidance and long‑term orientation (Chen et al., 2025).
* Suppression more adaptive in cultures emphasising restraint or collectivist norms (Chen et al., 2025).
* Cultural variation foreshadows how the EPM’s identification and selection stages are culturally embedded.
* Cultural norms play a decisive role in shaping how individuals value regulatory goals within Gross's (2015) Extended Process Model (EPM), fundamentally influencing the trajectory of emotion regulation form identification through implementation. Because the EPM conceptualises regulation as a higher-order valuation process; one that evaluates an unfolding emotional response against contextually defined goals. Cultural norms become central in determining which goals are activated and how strongly they are prioristised. Gross (2015) notes that valuation systems are &quot;highly influenced by prior experience and contextual variables,&quot; and cultural norms constitute one of the most pervasive of these variables. Briley's (2014) dynamic constructivist perspective further clarifies that cultural knowledge is not monolithic but situationally activated: Individuals draw upon different cultural scripts depending on contextual cues, meaning that the valuation of regulatory goals within the EPM shifts fluidly across situations. This dynamic activation helps explain why the same strategy, such as suppression or reappraisal, can be valued positively in one cultural context and negatively in another.
* The outcomes of Chen et al.'s (2025) systematic review and meta-analysis provide particularly compelling evidence for how cultural norms shape the valuation and effectiveness of regulatory goals. Their findings demonstrate that suppression is more maladaptive in &quot;indulgent and competition-driven cultures,&quot; where emotional expression is tied to autonomy, authenticity, and personal agency. In these contexts, the higher-level valuation system is more likely to appraise suppression as misaligned with culturally valued goals, increasing the likelihood of negative psychological outcomes. Conversely, Chen et al. (2025) show that suppression is less harmful, and sometimes adaptive in interdependent cultural contexts where emotional restraint supports relational harmony. This pattern illustrates how cultural norms calibrate the perceived utility of regulatory strategies: When harmony is culturally valued, suppression aligns with regulatory goals and is therefore more readily selected and more effective. Their analysis also reveals that reappraisal tends to be more beneficial in cultures characterised by high uncertainty tolerance and short-term orientation, suggesting that cultural norms shape not only the desirability of particular strategies but also the cognitive framing through which emotional situations are interpreted. These findings map directly onto the EPM's valuation architecture: cultural norms influence the identification of regulatory need, the selection of a strategy that aligns with culturally valued goals, and the implementation of that strategy that aligns with culturally valued goals, and the implementation of that strategy in ways that are socially coherent.
* Cultural norms sculpt the goals that guide higher-order valuation systems. determining when regulation is necessary, which strategies are valued, and how regulatory success is defined. Ultimate, cultural norms do not merely influence strategy choice, they shape the very architecture of emotional regulation, determining the meaning, purpose, and consequences of regulatory action.

== Cognitive Flexibility in Emotional Regulation ==

* Regulatory flexibility requires context sensitivity, a diverse repertoire, and responsiveness to feedback (Bonanno &amp; Burton, 2013).
* Cognitive flexibility supports adaptive switching when strategies prove ineffective.
* Physiological markers (e.g., corrugator EMG, LPP, SPN) predict switching decisions, indicating cognitive‑affective monitoring processes (Adamczyk et al., 2024).
* Flexibility explains individual differences in regulatory effectiveness beyond strategy type.
* Leads into the question: ''What role does cognitive flexibility play in the EPM’s ability to explain individual differences in regulatory effectiveness?''

== Children and Emotional Regulation ==

* Children demonstrate early regulatory flexibility, including spontaneous strategy use and switching (Wong et al., 2019).
* Age increases likelihood of cognitively demanding strategies such as reappraisal (Wong et al., 2019).
* Negative emotion intensity prompts greater use of disengagement strategies like distraction (Wong et al., 2019).
* Developmental patterns highlight how identification and selection processes mature across childhood.
* Provides developmental context for understanding dysregulation in clinical groups.
* Dysregulation strongly predicts anxiety in autistic youth, independent of core symptoms (Conner et al., 2020).
* Leads into the question: ''how does EPM explain the strong predictive link between emotional dysregulation and anxiety in autistic youth?''

== What Emotional Regulation Strategies are Most Effective ==

* Reappraisal generally linked to better mental health outcomes; suppression linked to poorer outcomes, though context moderates these effects (Chen et al., 2025).
* Distraction and reappraisal reduce negative affect but operate through distinct attentional and cognitive mechanisms (Strauss et al., 2016).
* Switching to distraction improves neural downregulation; switching to reappraisal can impair it under high‑intensity conditions (Adamczyk et al., 2024).
* Leads into the question: ''In what situations does switching to distraction improve outcomes, and why might switching to reappraisal impair them?''

==Conclusion==
* Emotional regulation is a dunamic, multi-stage system invovling '''identification, selection,''' and '''implementation''' of regulatory strategies (Gross, 2015)
* The EPM conceptualises regulation as a higher-order valuation process, continuously monitoring emotional states and adjusting strategies based on contextual feedback (Gross, 2015)
* Regulation is not inherently adaptive or maladaptive; it's effectiveness depends on contextual affordances, cognitive resources and situational demands (Gross, 2015)
* EPM provides a mechanistic framework explaining why individuals differ in regulatory success, integrating cognitive flexibility, context sensitivity and strategy repertoire (Bonanno &amp; Burton, 2013). 
* EPM offers a structure for understanding cross-cultural variation in regulatory goals and strategy valuation (Chen et al., 2025)

{{tip|Take Home Messages:
* Effective emotion regulation is flexible, not fixed; adaptability is more important than any single strategy.
* Cultural norms, cognitive flexibility, and developmental factors shape how regulation unfolds
* Dysregulation is a powerful predictor of mental health difficulties, reinforcing the need for models like the EPM to guide intervention
* Strategy effectiveness is context-dependent
* The EPM provides a cohesive, empirically grounded framework for understanding the complexity of human emotional life
}}

== See also ==
{{expand}}

==References==
{{Hanging indent|1=

Adamczyk, A. K., et al. (2024). Emotion regulation flexibility: EEG, EMG predictors and consequences of switching. Psychophysiology, 61(7). https://doi.org/10.1111/psyp.14646

Bonanno, G. A., &amp; Burton, C. L. (2013). Regulatory flexibility: An individual differences perspective on coping and emotion regulation. Perspectives on Psychological Science, 8(6), 591–612.

Chen, X., Cai, Q., Omari, D., Sanghvi, D. E., Lyu, S., &amp; Bonanno, G. A. (2025). Emotion regulation and mental health across cultures: A systematic review and meta-analysis. Nature Human Behaviour. https://doi.org/10.1038/s41562-025-02168-8 (doi.org in Bing)

Conner, C. M., et al. (2020). The role of emotion regulation and core autism symptoms in the experience of anxiety in autism. Autism, 24(4), 931–940.

Gross, J. J. (2015). The extended process model of emotion regulation: Elaborations, applications, and future directions. Psychological Inquiry, 26(1), 130–137.

Strauss, G. P., Ossenfort, K. L., &amp; Whearty, K. M. (2016). Reappraisal and distraction emotion regulation strategies are associated with distinct patterns of visual attention and differing levels of cognitive demand. PLoS ONE, 11(11), e0162290.

Wong, P. S., et al. (2019). Emotion regulation strategies in children: Developmental patterns and cognitive mechanisms. Journal of Experimental Child Psychology, 183, 1–18.

}}

== External links ==
{{expand}}

{{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

[https://www.youtube.com/watch?v=gAMbkJk6gnE What are emotions? and why do we feel them?]

[https://www.youtube.com/watch?v=Yd6hR1qCfSM Emotion Regulation with James J. Gross, PhD]

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]</text>
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    </revision>
    <revision>
      <id>2833717</id>
      <parentid>2833716</parentid>
      <timestamp>2026-09-18T06:32:03Z</timestamp>
      <contributor>
        <username>TheHutt02</username>
        <id>3106996</id>
      </contributor>
      <comment>Getting rid of previous scaffolding dot points</comment>
      <origin>2833717</origin>
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      <text bytes="16521" sha1="je9ynf8kq6q2q1ihyveynj6kff5ez2u" xml:space="preserve">{{title|Extended process model of emotion regulation:&lt;br&gt;What is the extended process model and how does it explain the regulation of emotions in different contexts?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=6}}
[[File:School level test of Wikischolar 2026 at Ispahani Public School &amp; College 08.jpg|thumb|'''Figure 1'''. Stressful exam {{ic|Consider expanding this figure caption to make the connection to the scenario more clear}}]]

''' Case Study - Exam stressors'''

Michael is halfway through a university exam, in a small classroom filled with 30 other examinees. Suddenly, he realises that he misread a question and wasted the past 15 minutes. His heat{{sp}} rate spikes, thoughts start racing and {{missing}} begins to panic. Becoming overwhelmed at the sudden onset of negativity, he felt{{g}} the urge to give up.

Normally, Michael copes with [[W: Psychological stress | stress]] and [[anxiety]] through exercise as he finds this is the most consistent modulator for his emotions. But in an exam room, this strategy becomes moot.

Michael stops, realises that the current negativity isn't helping his situation, and identifies that panic is only hindering his performance and that emotional regulation is needed if he wants to do well. He starts to tell himself &quot;I can still get partial marks for that question&quot;. Realising that the positive self-talk is helping he continues &quot;On this next question I'll make sure to focus on all facet's{{g}} of what the question asks&quot;. By the end of the next question Michael once again felt a sense of confidence in his ability to pass the exam.
{{RoundBoxBottom}}

Emotion regulation refers to the processes through which individuals monitor, evaluate and modify their emotional responses {{ic|APA style uses serial commas}}. Contemporary psychological science emphasises that regulation is not a singular act but a dynamic, context-sensitive system continuously unfolding over time (Bonanno &amp; Burton, 2013). Gross's (2015) Extended Process Model (EPM) captures this complexity by organising regulation into three iterative stages: identification, selection and implementation. Each governed by a higher-order valuation system that determines whether, when, and how emotions should be regulated. This framework highlights that regulatory success depends not only on the strategy chosen but on the fit between regulatory goals, contextual affordances, and the individual's cognitive resources.

Emotional regulation is central to mental health. [[Motivation and emotion/Book/2026/Emotion dysregulation|Emotional dysregulation]] predicts a wide range of difficulties, including the strong associated between dysregulation and anxiety in autistic youth (Connor et al., 2020). Meta-analytic evidence further demonstrates that habitual reappraisal is linked to better wellbeing, whereas suppression is often linked to poorer outcomes, though these patterns seem to vary across contexts (Chen et al., 2025). These findings underscore the need to understand ''why'' emotional regulation works differently across individuals and situations.

{{RoundBoxTop|theme=6}}
'''Focus questions'''

* How do cultural [[W: social norms | norms]] shape the valuation of regulatory goals within the EPM?
* What role does [[W: cognitive flexibility | cognitive flexibility]] play in the EPM’s ability to explain individual differences in regulatory effectiveness?
* How does the EPM explain the strong predictive link between [[Motivation and emotion/Book/2026/Emotion dysregulation | emotional dysregulation]] and anxiety in autistic youth?
* In what types of situations does switching to distraction improve regulatory outcomes, and why might switching to [[W: cognitive appraisal |reappraisal ]] impair them?

{{RoundBoxBottom}}

== The Extended Process Model of Emotional Regulation ==

* Emotion regulation as a higher‑order valuation system modifying first‑order emotional responses (Gross, 2015).
* Three‑stage regulatory cycle: '''identification''', '''selection''', '''implementation''' (Gross, 2015).
** Identification: The identification stage concerns the fundamental question of whether emotion regulation is required at all. According to Gross (2015), this stage is governed by a higher-order valuation system (explain this and then edit the dot points above) that evaluates the unfolding emotional response against current goals, contextual affordances, and motivational priorities. Identification involves detecting discrepancies between desired and actual emotional states. Essentially, recognising that the current, experienced emotion is misaligned with what the situation demands. This is an evaluative process, integrating prior learning, cultural norms and situational constraints to determine the necessity of regulation. Failure at this stage, such as misidentifying an emotion as irrelevant or failing to recognise a maladaptive trajectory can derailed the entire regulatory cycle. Thus, the identification stage acts as the gatekeeper of emotional regulation, ensuring cognitive resources are deployed only when emotional change is instrumentally valuable.
** Selection: Once regulation is deemed necessary, the selection stage determines what strategy should be used. Gross (2015) emphasises that this stage involves choosing among diverse regulatory families, such as attentional deployment, cognitive change, or response modulation, based on their anticipated fit with situational demands. Selection is a predictive process; the valuation system simulates the likely consequences of each strategy, weighing cognitive costs, contextual differences in regulatory repertoire (Bonanno &amp; Burton, 2013), meaning that people with broader, more flexible strategy selection requires both contextual sensitivity and strategic foresight; poor selection may lead to strategies that are cognitively overtaxing, situationally inappropriate, or counterproductive. In this way, selection acts as the model's optimisation mechanism, aligning regulatory tactics with the dynamic structure of the emotional episode.
** Implementation: Implementation concerns ''how'' the chosen strategy is enacted in real time. Gross (2015) describes this stage as the translation of abstract regulatory intentions into concrete tactics, such as shifting attention, reframing meaning or modulating expressive behavior. Implementation is effortful and dynamic; it unfolds over time, requiring sustained cognitive control and continuous adjustment as the emotional episode evolves. Crucially, implementation is not a single action but an iterative process in which the tactic is maintained, intensified, or abandoned depending on its moment-to-moment effectiveness. Research has shown that ineffective implementation predicts strategy switching (Adamczyk et al., 20204), highlighting that implementation is tightly coupled with feedback processes. Thus, implementation is the engine of regulation, where theoretical  strategies become emboied actions that shape the emotional trajectory.
* Emphasis on temporal dynamics, regulation unfolds iteratively and adjusts based on feedback. - Maintenance
* Situated cognition: regulatory success depends on contextual affordances, not inherent strategy value (Gross, 2015).
* Sets the foundation for exploring cultural norms, cognitive flexibility, developmental trajectories, and strategy effectiveness.

&lt;quiz display=&quot;simple&quot;&gt;
{Which of these is not a stage in the regulatory cycle?|type =&quot;()&quot;}

+ Yelling 
- Identification
- Selection
- Implementation

{According to EPM, After Selecting One Strategy to Use, Emotional Regulation is Done: {{ic|Use sentence casing}}}

- True
+ False

{Improvements will be made to this quiz}

+ True
- False
&lt;/quiz&gt;

==The Effects of Culture on Emotional Regulation==

* Cultural norms play a decisive role in shaping how individuals value regulatory goals within Gross's (2015) Extended Process Model (EPM), fundamentally influencing the trajectory of emotion regulation form identification through implementation. Because the EPM conceptualises regulation as a higher-order valuation process; one that evaluates an unfolding emotional response against contextually defined goals. Cultural norms become central in determining which goals are activated and how strongly they are prioristised. Gross (2015) notes that valuation systems are &quot;highly influenced by prior experience and contextual variables,&quot; and cultural norms constitute one of the most pervasive of these variables. Briley's (2014) dynamic constructivist perspective further clarifies that cultural knowledge is not monolithic but situationally activated: Individuals draw upon different cultural scripts depending on contextual cues, meaning that the valuation of regulatory goals within the EPM shifts fluidly across situations. This dynamic activation helps explain why the same strategy, such as suppression or reappraisal, can be valued positively in one cultural context and negatively in another.
* The outcomes of Chen et al.'s (2025) systematic review and meta-analysis provide particularly compelling evidence for how cultural norms shape the valuation and effectiveness of regulatory goals. Their findings demonstrate that suppression is more maladaptive in &quot;indulgent and competition-driven cultures,&quot; where emotional expression is tied to autonomy, authenticity, and personal agency. In these contexts, the higher-level valuation system is more likely to appraise suppression as misaligned with culturally valued goals, increasing the likelihood of negative psychological outcomes. Conversely, Chen et al. (2025) show that suppression is less harmful, and sometimes adaptive in interdependent cultural contexts where emotional restraint supports relational harmony. This pattern illustrates how cultural norms calibrate the perceived utility of regulatory strategies: When harmony is culturally valued, suppression aligns with regulatory goals and is therefore more readily selected and more effective. Their analysis also reveals that reappraisal tends to be more beneficial in cultures characterised by high uncertainty tolerance and short-term orientation, suggesting that cultural norms shape not only the desirability of particular strategies but also the cognitive framing through which emotional situations are interpreted. These findings map directly onto the EPM's valuation architecture: cultural norms influence the identification of regulatory need, the selection of a strategy that aligns with culturally valued goals, and the implementation of that strategy that aligns with culturally valued goals, and the implementation of that strategy in ways that are socially coherent.
* Cultural norms sculpt the goals that guide higher-order valuation systems. determining when regulation is necessary, which strategies are valued, and how regulatory success is defined. Ultimate, cultural norms do not merely influence strategy choice, they shape the very architecture of emotional regulation, determining the meaning, purpose, and consequences of regulatory action.

== Cognitive Flexibility in Emotional Regulation ==

* Regulatory flexibility requires context sensitivity, a diverse repertoire, and responsiveness to feedback (Bonanno &amp; Burton, 2013).
* Cognitive flexibility supports adaptive switching when strategies prove ineffective.
* Physiological markers (e.g., corrugator EMG, LPP, SPN) predict switching decisions, indicating cognitive‑affective monitoring processes (Adamczyk et al., 2024).
* Flexibility explains individual differences in regulatory effectiveness beyond strategy type.
* Leads into the question: ''What role does cognitive flexibility play in the EPM’s ability to explain individual differences in regulatory effectiveness?''

== Children and Emotional Regulation ==

* Children demonstrate early regulatory flexibility, including spontaneous strategy use and switching (Wong et al., 2019).
* Age increases likelihood of cognitively demanding strategies such as reappraisal (Wong et al., 2019).
* Negative emotion intensity prompts greater use of disengagement strategies like distraction (Wong et al., 2019).
* Developmental patterns highlight how identification and selection processes mature across childhood.
* Provides developmental context for understanding dysregulation in clinical groups.
* Dysregulation strongly predicts anxiety in autistic youth, independent of core symptoms (Conner et al., 2020).
* Leads into the question: ''how does EPM explain the strong predictive link between emotional dysregulation and anxiety in autistic youth?''

== What Emotional Regulation Strategies are Most Effective ==

* Reappraisal generally linked to better mental health outcomes; suppression linked to poorer outcomes, though context moderates these effects (Chen et al., 2025).
* Distraction and reappraisal reduce negative affect but operate through distinct attentional and cognitive mechanisms (Strauss et al., 2016).
* Switching to distraction improves neural downregulation; switching to reappraisal can impair it under high‑intensity conditions (Adamczyk et al., 2024).
* Leads into the question: ''In what situations does switching to distraction improve outcomes, and why might switching to reappraisal impair them?''

==Conclusion==
* Emotional regulation is a dunamic, multi-stage system invovling '''identification, selection,''' and '''implementation''' of regulatory strategies (Gross, 2015)
* The EPM conceptualises regulation as a higher-order valuation process, continuously monitoring emotional states and adjusting strategies based on contextual feedback (Gross, 2015)
* Regulation is not inherently adaptive or maladaptive; it's effectiveness depends on contextual affordances, cognitive resources and situational demands (Gross, 2015)
* EPM provides a mechanistic framework explaining why individuals differ in regulatory success, integrating cognitive flexibility, context sensitivity and strategy repertoire (Bonanno &amp; Burton, 2013). 
* EPM offers a structure for understanding cross-cultural variation in regulatory goals and strategy valuation (Chen et al., 2025)

{{tip|Take Home Messages:
* Effective emotion regulation is flexible, not fixed; adaptability is more important than any single strategy.
* Cultural norms, cognitive flexibility, and developmental factors shape how regulation unfolds
* Dysregulation is a powerful predictor of mental health difficulties, reinforcing the need for models like the EPM to guide intervention
* Strategy effectiveness is context-dependent
* The EPM provides a cohesive, empirically grounded framework for understanding the complexity of human emotional life
}}

== See also ==
{{expand}}

==References==
{{Hanging indent|1=

Adamczyk, A. K., et al. (2024). Emotion regulation flexibility: EEG, EMG predictors and consequences of switching. Psychophysiology, 61(7). https://doi.org/10.1111/psyp.14646

Bonanno, G. A., &amp; Burton, C. L. (2013). Regulatory flexibility: An individual differences perspective on coping and emotion regulation. Perspectives on Psychological Science, 8(6), 591–612.

Chen, X., Cai, Q., Omari, D., Sanghvi, D. E., Lyu, S., &amp; Bonanno, G. A. (2025). Emotion regulation and mental health across cultures: A systematic review and meta-analysis. Nature Human Behaviour. https://doi.org/10.1038/s41562-025-02168-8 (doi.org in Bing)

Conner, C. M., et al. (2020). The role of emotion regulation and core autism symptoms in the experience of anxiety in autism. Autism, 24(4), 931–940.

Gross, J. J. (2015). The extended process model of emotion regulation: Elaborations, applications, and future directions. Psychological Inquiry, 26(1), 130–137.

Strauss, G. P., Ossenfort, K. L., &amp; Whearty, K. M. (2016). Reappraisal and distraction emotion regulation strategies are associated with distinct patterns of visual attention and differing levels of cognitive demand. PLoS ONE, 11(11), e0162290.

Wong, P. S., et al. (2019). Emotion regulation strategies in children: Developmental patterns and cognitive mechanisms. Journal of Experimental Child Psychology, 183, 1–18.

}}

== External links ==
{{expand}}

{{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

[https://www.youtube.com/watch?v=gAMbkJk6gnE What are emotions? and why do we feel them?]

[https://www.youtube.com/watch?v=Yd6hR1qCfSM Emotion Regulation with James J. Gross, PhD]

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]</text>
      <sha1>je9ynf8kq6q2q1ihyveynj6kff5ez2u</sha1>
    </revision>
    <revision>
      <id>2833718</id>
      <parentid>2833717</parentid>
      <timestamp>2026-09-18T06:33:29Z</timestamp>
      <contributor>
        <username>TheHutt02</username>
        <id>3106996</id>
      </contributor>
      <comment>Writing down an idea as to not forget</comment>
      <origin>2833718</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16600" sha1="s6hwmlgu9wuoqg01vscg8ntkx9my1fz" xml:space="preserve">{{title|Extended process model of emotion regulation:&lt;br&gt;What is the extended process model and how does it explain the regulation of emotions in different contexts?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=6}}
[[File:School level test of Wikischolar 2026 at Ispahani Public School &amp; College 08.jpg|thumb|'''Figure 1'''. Stressful exam {{ic|Consider expanding this figure caption to make the connection to the scenario more clear}}]]

''' Case Study - Exam stressors'''

Michael is halfway through a university exam, in a small classroom filled with 30 other examinees. Suddenly, he realises that he misread a question and wasted the past 15 minutes. His heat{{sp}} rate spikes, thoughts start racing and {{missing}} begins to panic. Becoming overwhelmed at the sudden onset of negativity, he felt{{g}} the urge to give up.

Normally, Michael copes with [[W: Psychological stress | stress]] and [[anxiety]] through exercise as he finds this is the most consistent modulator for his emotions. But in an exam room, this strategy becomes moot.

Michael stops, realises that the current negativity isn't helping his situation, and identifies that panic is only hindering his performance and that emotional regulation is needed if he wants to do well. He starts to tell himself &quot;I can still get partial marks for that question&quot;. Realising that the positive self-talk is helping he continues &quot;On this next question I'll make sure to focus on all facet's{{g}} of what the question asks&quot;. By the end of the next question Michael once again felt a sense of confidence in his ability to pass the exam.
{{RoundBoxBottom}}

Emotion regulation refers to the processes through which individuals monitor, evaluate and modify their emotional responses {{ic|APA style uses serial commas}}. Contemporary psychological science emphasises that regulation is not a singular act but a dynamic, context-sensitive system continuously unfolding over time (Bonanno &amp; Burton, 2013). Gross's (2015) Extended Process Model (EPM) captures this complexity by organising regulation into three iterative stages: identification, selection and implementation. Each governed by a higher-order valuation system that determines whether, when, and how emotions should be regulated. This framework highlights that regulatory success depends not only on the strategy chosen but on the fit between regulatory goals, contextual affordances, and the individual's cognitive resources.

Emotional regulation is central to mental health. [[Motivation and emotion/Book/2026/Emotion dysregulation|Emotional dysregulation]] predicts a wide range of difficulties, including the strong associated between dysregulation and anxiety in autistic youth (Connor et al., 2020). Meta-analytic evidence further demonstrates that habitual reappraisal is linked to better wellbeing, whereas suppression is often linked to poorer outcomes, though these patterns seem to vary across contexts (Chen et al., 2025). These findings underscore the need to understand ''why'' emotional regulation works differently across individuals and situations.

{{RoundBoxTop|theme=6}}
'''Focus questions'''

* How do cultural [[W: social norms | norms]] shape the valuation of regulatory goals within the EPM?
* What role does [[W: cognitive flexibility | cognitive flexibility]] play in the EPM’s ability to explain individual differences in regulatory effectiveness?
* How does the EPM explain the strong predictive link between [[Motivation and emotion/Book/2026/Emotion dysregulation | emotional dysregulation]] and anxiety in autistic youth?
* In what types of situations does switching to distraction improve regulatory outcomes, and why might switching to [[W: cognitive appraisal |reappraisal ]] impair them?

{{RoundBoxBottom}}

== The Extended Process Model of Emotional Regulation ==

* Emotion regulation as a higher‑order valuation system modifying first‑order emotional responses (Gross, 2015).
* Three‑stage regulatory cycle: '''identification''', '''selection''', '''implementation''' (Gross, 2015).
** Identification: The identification stage concerns the fundamental question of whether emotion regulation is required at all. According to Gross (2015), this stage is governed by a higher-order valuation system (explain this and then edit the dot points above) that evaluates the unfolding emotional response against current goals, contextual affordances, and motivational priorities. Identification involves detecting discrepancies between desired and actual emotional states. Essentially, recognising that the current, experienced emotion is misaligned with what the situation demands. This is an evaluative process, integrating prior learning, cultural norms and situational constraints to determine the necessity of regulation. Failure at this stage, such as misidentifying an emotion as irrelevant or failing to recognise a maladaptive trajectory can derailed the entire regulatory cycle. Thus, the identification stage acts as the gatekeeper of emotional regulation, ensuring cognitive resources are deployed only when emotional change is instrumentally valuable.
** Selection: Once regulation is deemed necessary, the selection stage determines what strategy should be used. Gross (2015) emphasises that this stage involves choosing among diverse regulatory families, such as attentional deployment, cognitive change, or response modulation, based on their anticipated fit with situational demands. Selection is a predictive process; the valuation system simulates the likely consequences of each strategy, weighing cognitive costs, contextual differences in regulatory repertoire (Bonanno &amp; Burton, 2013), meaning that people with broader, more flexible strategy selection requires both contextual sensitivity and strategic foresight; poor selection may lead to strategies that are cognitively overtaxing, situationally inappropriate, or counterproductive. In this way, selection acts as the model's optimisation mechanism, aligning regulatory tactics with the dynamic structure of the emotional episode.
** Implementation: Implementation concerns ''how'' the chosen strategy is enacted in real time. Gross (2015) describes this stage as the translation of abstract regulatory intentions into concrete tactics, such as shifting attention, reframing meaning or modulating expressive behavior. Implementation is effortful and dynamic; it unfolds over time, requiring sustained cognitive control and continuous adjustment as the emotional episode evolves. Crucially, implementation is not a single action but an iterative process in which the tactic is maintained, intensified, or abandoned depending on its moment-to-moment effectiveness. Research has shown that ineffective implementation predicts strategy switching (Adamczyk et al., 20204), highlighting that implementation is tightly coupled with feedback processes. Thus, implementation is the engine of regulation, where theoretical  strategies become emboied actions that shape the emotional trajectory.
* Emphasis on temporal dynamics, regulation unfolds iteratively and adjusts based on feedback. - Maintenance
* Situated cognition: regulatory success depends on contextual affordances, not inherent strategy value (Gross, 2015).
* Sets the foundation for exploring cultural norms, cognitive flexibility, developmental trajectories, and strategy effectiveness.


Idea: put table here with a summary of the stages of EPM, move quiz elsewhere.&lt;quiz display=&quot;simple&quot;&gt;
{Which of these is not a stage in the regulatory cycle?|type =&quot;()&quot;}

+ Yelling 
- Identification
- Selection
- Implementation

{According to EPM, After Selecting One Strategy to Use, Emotional Regulation is Done: {{ic|Use sentence casing}}}

- True
+ False

{Improvements will be made to this quiz}

+ True
- False
&lt;/quiz&gt;

==The Effects of Culture on Emotional Regulation==

* Cultural norms play a decisive role in shaping how individuals value regulatory goals within Gross's (2015) Extended Process Model (EPM), fundamentally influencing the trajectory of emotion regulation form identification through implementation. Because the EPM conceptualises regulation as a higher-order valuation process; one that evaluates an unfolding emotional response against contextually defined goals. Cultural norms become central in determining which goals are activated and how strongly they are prioristised. Gross (2015) notes that valuation systems are &quot;highly influenced by prior experience and contextual variables,&quot; and cultural norms constitute one of the most pervasive of these variables. Briley's (2014) dynamic constructivist perspective further clarifies that cultural knowledge is not monolithic but situationally activated: Individuals draw upon different cultural scripts depending on contextual cues, meaning that the valuation of regulatory goals within the EPM shifts fluidly across situations. This dynamic activation helps explain why the same strategy, such as suppression or reappraisal, can be valued positively in one cultural context and negatively in another.
* The outcomes of Chen et al.'s (2025) systematic review and meta-analysis provide particularly compelling evidence for how cultural norms shape the valuation and effectiveness of regulatory goals. Their findings demonstrate that suppression is more maladaptive in &quot;indulgent and competition-driven cultures,&quot; where emotional expression is tied to autonomy, authenticity, and personal agency. In these contexts, the higher-level valuation system is more likely to appraise suppression as misaligned with culturally valued goals, increasing the likelihood of negative psychological outcomes. Conversely, Chen et al. (2025) show that suppression is less harmful, and sometimes adaptive in interdependent cultural contexts where emotional restraint supports relational harmony. This pattern illustrates how cultural norms calibrate the perceived utility of regulatory strategies: When harmony is culturally valued, suppression aligns with regulatory goals and is therefore more readily selected and more effective. Their analysis also reveals that reappraisal tends to be more beneficial in cultures characterised by high uncertainty tolerance and short-term orientation, suggesting that cultural norms shape not only the desirability of particular strategies but also the cognitive framing through which emotional situations are interpreted. These findings map directly onto the EPM's valuation architecture: cultural norms influence the identification of regulatory need, the selection of a strategy that aligns with culturally valued goals, and the implementation of that strategy that aligns with culturally valued goals, and the implementation of that strategy in ways that are socially coherent.
* Cultural norms sculpt the goals that guide higher-order valuation systems. determining when regulation is necessary, which strategies are valued, and how regulatory success is defined. Ultimate, cultural norms do not merely influence strategy choice, they shape the very architecture of emotional regulation, determining the meaning, purpose, and consequences of regulatory action.

== Cognitive Flexibility in Emotional Regulation ==

* Regulatory flexibility requires context sensitivity, a diverse repertoire, and responsiveness to feedback (Bonanno &amp; Burton, 2013).
* Cognitive flexibility supports adaptive switching when strategies prove ineffective.
* Physiological markers (e.g., corrugator EMG, LPP, SPN) predict switching decisions, indicating cognitive‑affective monitoring processes (Adamczyk et al., 2024).
* Flexibility explains individual differences in regulatory effectiveness beyond strategy type.
* Leads into the question: ''What role does cognitive flexibility play in the EPM’s ability to explain individual differences in regulatory effectiveness?''

== Children and Emotional Regulation ==

* Children demonstrate early regulatory flexibility, including spontaneous strategy use and switching (Wong et al., 2019).
* Age increases likelihood of cognitively demanding strategies such as reappraisal (Wong et al., 2019).
* Negative emotion intensity prompts greater use of disengagement strategies like distraction (Wong et al., 2019).
* Developmental patterns highlight how identification and selection processes mature across childhood.
* Provides developmental context for understanding dysregulation in clinical groups.
* Dysregulation strongly predicts anxiety in autistic youth, independent of core symptoms (Conner et al., 2020).
* Leads into the question: ''how does EPM explain the strong predictive link between emotional dysregulation and anxiety in autistic youth?''

== What Emotional Regulation Strategies are Most Effective ==

* Reappraisal generally linked to better mental health outcomes; suppression linked to poorer outcomes, though context moderates these effects (Chen et al., 2025).
* Distraction and reappraisal reduce negative affect but operate through distinct attentional and cognitive mechanisms (Strauss et al., 2016).
* Switching to distraction improves neural downregulation; switching to reappraisal can impair it under high‑intensity conditions (Adamczyk et al., 2024).
* Leads into the question: ''In what situations does switching to distraction improve outcomes, and why might switching to reappraisal impair them?''

==Conclusion==
* Emotional regulation is a dunamic, multi-stage system invovling '''identification, selection,''' and '''implementation''' of regulatory strategies (Gross, 2015)
* The EPM conceptualises regulation as a higher-order valuation process, continuously monitoring emotional states and adjusting strategies based on contextual feedback (Gross, 2015)
* Regulation is not inherently adaptive or maladaptive; it's effectiveness depends on contextual affordances, cognitive resources and situational demands (Gross, 2015)
* EPM provides a mechanistic framework explaining why individuals differ in regulatory success, integrating cognitive flexibility, context sensitivity and strategy repertoire (Bonanno &amp; Burton, 2013). 
* EPM offers a structure for understanding cross-cultural variation in regulatory goals and strategy valuation (Chen et al., 2025)

{{tip|Take Home Messages:
* Effective emotion regulation is flexible, not fixed; adaptability is more important than any single strategy.
* Cultural norms, cognitive flexibility, and developmental factors shape how regulation unfolds
* Dysregulation is a powerful predictor of mental health difficulties, reinforcing the need for models like the EPM to guide intervention
* Strategy effectiveness is context-dependent
* The EPM provides a cohesive, empirically grounded framework for understanding the complexity of human emotional life
}}

== See also ==
{{expand}}

==References==
{{Hanging indent|1=

Adamczyk, A. K., et al. (2024). Emotion regulation flexibility: EEG, EMG predictors and consequences of switching. Psychophysiology, 61(7). https://doi.org/10.1111/psyp.14646

Bonanno, G. A., &amp; Burton, C. L. (2013). Regulatory flexibility: An individual differences perspective on coping and emotion regulation. Perspectives on Psychological Science, 8(6), 591–612.

Chen, X., Cai, Q., Omari, D., Sanghvi, D. E., Lyu, S., &amp; Bonanno, G. A. (2025). Emotion regulation and mental health across cultures: A systematic review and meta-analysis. Nature Human Behaviour. https://doi.org/10.1038/s41562-025-02168-8 (doi.org in Bing)

Conner, C. M., et al. (2020). The role of emotion regulation and core autism symptoms in the experience of anxiety in autism. Autism, 24(4), 931–940.

Gross, J. J. (2015). The extended process model of emotion regulation: Elaborations, applications, and future directions. Psychological Inquiry, 26(1), 130–137.

Strauss, G. P., Ossenfort, K. L., &amp; Whearty, K. M. (2016). Reappraisal and distraction emotion regulation strategies are associated with distinct patterns of visual attention and differing levels of cognitive demand. PLoS ONE, 11(11), e0162290.

Wong, P. S., et al. (2019). Emotion regulation strategies in children: Developmental patterns and cognitive mechanisms. Journal of Experimental Child Psychology, 183, 1–18.

}}

== External links ==
{{expand}}

{{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

[https://www.youtube.com/watch?v=gAMbkJk6gnE What are emotions? and why do we feel them?]

[https://www.youtube.com/watch?v=Yd6hR1qCfSM Emotion Regulation with James J. Gross, PhD]

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotional self-regulation]]</text>
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      <text bytes="7635" sha1="smhtqre55w7tehzduccy1exst8f4ktx" xml:space="preserve">== About Me ==
I am a military veteran, working to complete a Bachelor of Science in Psychology as part of a lifelong approach to learning. After a military career working with people around the world on a spectrum of operations, I wanted to better understand the human dimension and the science behind what makes us all tick. Along the way, I want to give back to the community where I can. I have an interest in veterans' PTSD, advocacy and international affairs.

== Book Chapter ==
[[File:PTSD.png|left|thumb|250x250px|'''Figure 1.''' PTSD can have a deep and lasting impact on our emotions.]]
I am writing a book chapter titled [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|Immersive Therapy for PTSD: How does it work and what are the effects?]] 

This chapter is an individual student contribution as part of a larger [https://www.canberra.edu.au/ University of Canberra] class effort in 2026 to write a book [[Motivation and emotion/Book]]. 

The 2026 book extends a Wikiversity book series started in 2010, with over 1,800 online book chapters on how psychological science can improve human lives.

The book editor and University psychology unit convener is [[User:Jtneill|Dr. James Neill]]
{{clear}}

== Social Contributions ==

#'''18 Aug 26:''' Grammar and content editing improvements on 2025 chapter, Defence mechanisms and emotion regulation. Edits at https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FDefence_mechanisms_and_emotion_regulation&amp;diff=2822629&amp;oldid=2763661
# '''18 Aug 26:''' Grammar and content editing improvements on 2025 chapter, Neurodivergence and trauma. Edits at https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FNeurodivergence_and_trauma&amp;diff=2822636&amp;oldid=2812805
# '''19 Aug 26:''' Grammar and content editing improvements on 2025 chapter, Incentive theory of motivation. Edits at&lt;nowiki/&gt;https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FIncentive_theory_of_motivation&amp;diff=2822844&amp;oldid=2814898
# '''19 Aug 26:''' UC Canvas Discussion: Introduced the book chapter intent to the class and welcomed anyone with sim&lt;nowiki/&gt;ilar topics or interests to contribute. I offered the same. https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456450
# '''20 Aug 26:''' Comment: Supported another Wiki user by providing some peer-reviewed ideas on starter references f&lt;nowiki/&gt;or a Chapter page. [[Talk:Motivation and emotion/Book/2026/Perfectionism and procrastination#Reference material]]
# '''20 Aug 26:''' Comment: Supported another Wiki user by providing some peer-reviewed ideas on starter references f&lt;nowiki/&gt;or a Chapter page.[[Talk:Motivation and emotion/Book/2026/Irritability#Reference material]]
# '''22 Aug 26:''' Grammar and content editing improvements on 2025 chapter, Mental health in astronauts. Edits at [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FMental_health_in_astronauts&amp;diff=2824159&amp;oldid=2804667 ht]&lt;nowiki/&gt;[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FMental_health_in_astronauts&amp;diff=2824159&amp;oldid=2804667 tps://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FMental_health_in_astronauts&amp;diff=2824159&amp;oldid=2804667]
# '''25 Aug 26:''' Comment: Supported another Wiki user by providing some peer-reviewed ideas on starter references f&lt;nowiki/&gt;or a Chapter page.[[Talk:Motivation and emotion/Book/2026/Feedback literacy#Reference]]
# '''25 Aug 26''': UC Canvas Discussion: Responded to student topic query.[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457190 https://uclearn.canberra.edu.au/courses/201]&lt;nowiki/&gt;[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457190 43/discussion_topics/457190]
# '''26 Aug 26:''' Comment: Supported another Wiki user by providing some external link ideas for a Chapter page.[[Talk:Motivation and emotion/Book/2026/Dark empathy#Reference|Talk]]&lt;nowiki/&gt;[[Talk:Motivation and emotion/Book/2026/Dark empathy#Reference|:Motivation and emotion/Book/2026/Dark empathy#Reference]]
# '''26 Aug 26:''' UC Canvas Discussion: Responded to student topic query with data from a Random Game of Dice scenar&lt;nowiki/&gt;io.https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457412
# '''27 Aug 26:''' Wiki thanks and editing conversation: [[User talk:Jtneill#Punctuation change in book title]]
# '''28 Aug 26:''' UC Canvas Discussion: Responded to student topic query&lt;nowiki/&gt; https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457809
# '''4 Sep 26:''' Comment: Included creation of graphics for Wiki page.[[c:File:Avoidance_and_Processing_Cycles.png|ht]]&lt;nowiki/&gt;[[c:File:Avoidance_and_Processing_Cycles.png|tps://commons.wikimedia.org/wiki/File:Avoidance_and_Processing_Cycles.png]]
# '''4 Sep 26:''' Comment: Assisted other Wiki user by adding a quiz temp&lt;nowiki/&gt;late to their chapter page https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FBuilding_therapeutic_alliance&amp;diff=2831108&amp;oldid=2830050
# '''8 Sep 26:''' Comment: Assisted other Wiki user by adding a quiz temp&lt;nowiki/&gt;late to their chapter page https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FSelf-concept_and_motivation&amp;diff=2832141&amp;oldid=2831622
# '''9 Sep 26:''' Comment: Assisted another Wiki user by adding a quiz te&lt;nowiki/&gt;mplate to their chapter page&lt;nowiki/&gt;https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FOutdoor_play_and_children%27s_emotional_well-being&amp;diff=2832147&amp;oldid=2828722
# '''9 Sep 26:''' UC Canvas Discussion: Responded to student topic query &lt;nowiki/&gt;https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457888
# '''11 Sep 26:''' UC Canvas Discussion: Chapter word count question - in&lt;nowiki/&gt;cludes great response advice from other contributors on tools and techniques https://uclearn.canberra.edu.au/courses/20143/discussion_topics/461216
# '''14 Sep:''' Comment: Assisted another Wiki user by adding some advice&lt;nowiki/&gt; on prediction error references [[Talk:Motivation and emotion/Book/2026/Fear extinction#Prediction Error and Extinction]]
# '''15 Sep 26:''' Correspondence: Email exchange between chapter author &lt;nowiki/&gt;and Professor Vermetten, who is credited with creating the 3MDR therapy and referenced in the chapter.  &quot;I have looked at the Wikiversity page and think you are on the right path. You have brought together the concepts of immersion, embodiment, motivation, and trauma-focused treatment in a thoughtful and relevant way.&quot;
# '''16 Sep 26:''' Grammar and content editing improvements on 2025 chapt&lt;nowiki/&gt;er due to links with PTSD and prediction error ,https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FNeuroscience_of_unexpected_positive_outcomes&amp;diff=2833368&amp;oldid=2762078
# '''16 Sep 26:''' UC Canvas Discussion: Responded to student request for&lt;nowiki/&gt; chapter feedback on impulsivity and sensation seeking https://uclearn.canberra.edu.au/courses/20143/discussion_topics/461607
# '''16 Sep 26:''' UC Canvas Discussion: Responded to student request for&lt;nowiki/&gt; chapter feedback on brain implants for chronic pain&lt;nowiki/&gt;https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457902
# '''17 Sep 26:''' UC Canvas Discussion: Chapter referencing question abo&lt;nowiki/&gt;ut integration of non-academic journal sources neede&lt;nowiki/&gt;d to source financial market analysis relating to immersive PTSD forecasts. https://uclearn.canberra.edu.au/courses/20143/discussion_topics/462166</text>
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      <comment>/* Authors Statement */ updated link to AI chat record to demonstrate compliance with AI guidlines</comment>
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      <text bytes="9558" sha1="5hsgdunoqz1mcvqf3e7qmysvp3piuxf" xml:space="preserve">==Vermetten image==
{{ping|StretchBeyond}} You noted that &quot;(The Vermetten 2025 reading has an excellent flow chat to use if I can figure out how to get it embedded. the journal article is Creative Commons4.0 - need to ask James.&quot;
: If you can download the image, it can then be uploaded to [[commons:]] and embedded on Wikiversity. However, there is a catch. The license is CC-NC (Non-commercial) which restricts re-use. Wiki Commons only accepts media which are unrestricted for re-use (e.g., public domain or creative commons attribution). Unfortunately, this image couldn't, for example, be re-used in private enterprise. You could potentially create your own image inspired by the original, and then you own the copyright to that image and can upload/embed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:21, 18 August 2026 (UTC)

:Thank you. Based on what your advised yesterday, I have had an attempt at integrating some journal concepts into a graphic that I generated with Microsoft CoPilot. I have embedded it into my article now and referenced it in the caption, but I can't get the caption to be visual on the front page. I'm still struggling with how to manipulate figures and boxes, as the edits are not intuitive.  [[User:StretchBeyond|StretchBeyond]] ([[User talk:StretchBeyond|discuss]] • [[Special:Contributions/StretchBeyond|contribs]]) 08:34, 19 August 2026 (UTC)
: Well done! Hopefully, [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FImmersive_therapy_for_PTSD_treatment&amp;diff=2823045&amp;oldid=2823035 this] did the trick. The images are clickable through to the licensing etc., so those details don't need to be in the caption. After a while it will probably make sense to use &quot;edit source&quot; which gives more editing control. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:51, 19 August 2026 (UTC)
::Thank you. I'll have some questions on this stuff tomorrow.  [[User:StretchBeyond|StretchBeyond]] ([[User talk:StretchBeyond|discuss]] • [[Special:Contributions/StretchBeyond|contribs]]) 08:55, 19 August 2026 (UTC)

== Strong topic development  ==

Just leaving some feedback, as this topic development chapter is genuinely excellent. The theory, mechanisms, and research evidence are integrated at a very high level, and the immersive therapy examples are clear and engaging. It’s one of the strongest drafts I’ve come across. The structure and flow are exceptionally strong, especially for a topic development stage. [[User:StudentUC2026|StudentUC2026]] ([[User talk:StudentUC2026|discuss]] • [[Special:Contributions/StudentUC2026|contribs]]) 10:22, 22 August 2026 (UTC)

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Clear [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]
# Remove links and citations from headings
# This chapter is likely to exceeed the maximum word count, so consider truncating preliminary material
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
|3=
&lt;!-- Overview--&gt;
# Very good
# Consider providing a compelling real-life or fictional scenario; costs could be cited in subsequent sections
# Consider abbreviating the problem description and moving detail into subsequent sections
# Reduce overcapitalisation; APA is a down-style: https://www.google.com.au/search?q=capitalization+site%3Aapastyle.apa.org
&lt;!-- Style --&gt;
# Use 3rd person point of view for focus questions
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Key points are well developed for each section
# Prelminary material (e.g., &quot;Why is emotional processing important in PTSD?&quot;)  will likely need to be abbreviated or removed to allow the chapter to concentrate on answering &quot;How does it work and what are the effects?&quot; within the maximimum word count
&lt;!-- Theory and research --&gt;
# Promising balance of theory and research

&lt;!-- Conclusion --&gt;
# Conclusion is well underway
# Concentrate on answering the focus questions
|5=
&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
&lt;!-- Creation --&gt;
# Well done on creating and uploading your own image! {{smile}}—this can also be listed on your user page as a social contribution
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
&lt;!-- Scenarios/examples/case studies --&gt;
# Promising use of scenarios/examples/case studies
# Keep scenarios brief 
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
# Keep quiz questions brief and embed them in the most relevant sections 
&lt;!-- Tables --&gt;
# Promising use of table(s)
# Table 1 is probably overly detailed; consider how to simplify
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Very good
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## [[Help:Wikitext quick reference|italicisation]]
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Good
## See in-text comment
&lt;!-- External links --&gt;
# External links
## Good
## See in-text comment
|9=
&lt;!-- User page --&gt;
# Excellent
&lt;!-- Description about self --&gt;
# Excellent description about self provided
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# Outstanding – at least three different types of contributions with direct link(s) to evidence
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:00, 29 August 2026 (UTC)

== Authors Statement ==
'''Authors Statement'''

''I certify that no part of this assignment has been copied from any other student’s work or from any other source except where due acknowledgement is made in the assignment. No part of this assignment has been written for me by any other person. The material contained in this assignment has not been previously submitted for assessment in any other formal unit of study.'' 

'''Gen AI Use Statement'''

''I have used the following Generative Artiﬁcial Intelligence (GenAI) tools/services in the preparation of this assessment:''

·       '''GenAI service name and version:''' Microsoft Copilot

·       '''Link to the GenAI service:''' https://copilot.microsoft.com/

·       '''Ways this GenAI service was used:''' for initial ideation in response to the topic and to brainstorm and develop a writing strategy for this material. Copilot was also used at the end of the process to compare the advanced draft against the rubric. Copilot was used to identify any gross logic errors or data discrepancies in the argument. Copilot was used to proofread the final reference list for APA 7 compliance after EndNote 21 automated it. https://m365.cloud.microsoft/chat/conversation/0895ffb5-6712-49d4-890d-1198212346ee?auth=2--[[User:StretchBeyond|StretchBeyond]] ([[User talk:StretchBeyond|discuss]] • [[Special:Contributions/StretchBeyond|contribs]]) 09:15, 18 September 2026 (UTC)

·       '''GenAI service name and version:''' University of Canberra Studiosity

·       '''Link to the GenAI service:''' https://studiosity.com/connect/partners/university-of-canberra/student_home

·       '''Ways this GenAI service was used:''' for university-sponsored AI feedback to improve written work prior to submission. This was particularly useful in maintaining logical flow through the paragraph PEEL structure and in some aspects of grammar improvement.

·       '''GenAI service name and version:''' Grammarly Desktop 2026 for Microsoft Word

·       '''Link to the GenAI service:''' https://www.grammarly.com/

'''Ways this GenAI service was used:''' I used an integrated MS Word Grammarly subscription to help edit grammar, writing clarity, and punctuation. The tool also assists with inadvertent plagiarism detection, ensuring that citations are sound. 

''I confirm that I have not used the Generative Artificial Intelligence service in the development of this work for assessment, other than as declared and acknowledged above, and that I have cited and referenced any GenAI content in my assessment submission, applying the relevant referencing style''. ''I understand that providing false or misleading information in this declaration and acknowledgement may constitute a breach of the'' [https://www.canberra.edu.au/about-uc/policy-and-legislation/legislation/rules/University-of-Canberra-Student-Conduct-Rules-2023.pdf University of Canberra (Student Conduct) Rules 2023.] [[User:StretchBeyond|StretchBeyond]] ([[User talk:StretchBeyond|discuss]] • [[Special:Contributions/StretchBeyond|contribs]]) 09:05, 16 September 2026 (UTC)</text>
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      <text bytes="16795" sha1="1tw25r6zuzlfllsn60w5h6fxj4g5s0a" xml:space="preserve">== About me ==
Hello Everyone,

I am currently a 3rd year psychology student at [https://www.google.com/search?client=safari&amp;rls=en&amp;q=University+of+canberra&amp;ie=UTF-8&amp;oe=UTF-8 University of Canberra] 

This semester I am studying [[Motivation and emotion|Motivation and Emotion]] unit.

My future goal is to become clinical psychologist and work with Australian Federal Police.

My Linkedln profile:  https://www.linkedin.com/in/palak-kathiriya-6b7048289/

Thank you for visiting my linkedln profile and this page!

== Hobbies ==

* Dancing
* Hiking
* Travelling to different countries 
* Painting 
* Cycling 
* Nature exploration
** Birdwatching
** Gardening 

== Book Chapter I'm working on ==
I am working on a really interesting topic for my book chapter. My chapter title is: Positive emotion dysregulation: What is positive emotion dysregulation and how does it affect psychological functioning? 

Link for my book chapter: [[Motivation and emotion/Book/2026/Positive emotion dysregulation|Positive emotion dysregulation]] 

== Social contributions ==
All times are in Canberra local time (AEST/AEDT)
# 12:58 pm, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FWarm-glow_giving&amp;diff=2826658&amp;oldid=2826657 Added the template and the title for this page - For this chapter: Warm-glow giving - Why does giving feel good and how does this influence prosocial behaviour? '''('''Book Chapter, 2026)]
# 11:59 am, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPerfectionism_and_procrastination&amp;diff=2826589&amp;oldid=2826579 Fixed spelling error in one of the focus question - For this chapter:  Perfectionism and procrastination - What is the role of perfectionism in procrastination and what can be done about it? (Book Chapter, 2026)]
# 12:28 pm, 26 August 2026: [[Talk:Motivation and emotion/Book/2026/Motivations for using sex work services#Heading casing|Made a suggestion about overview section - For this chapter: Motivations for using sex work services: What motivates use of sex work services? (Book Chapter, 2026)]]
# 2:03 pm, 26 August 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456558 Provided a couple of sources for the development of breathing exercises and relaxation book chapter (Book Chapter, 2026) (UC Learn)]
#8:10 am, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/458145 Commented on discussion forum about how to use GenAI in the unit and what are the expectations if we use GenAI (UC Learn)]
# 10:14 am , 2 September 2026:[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FSelf-control_and_ego_depletion_recovery&amp;diff=2830323&amp;oldid=2761410 Fixed spelling error in book chapter - For this chapter - Self-control and ego depletion recovery: How do people restore self-control resources after depletion and what factors influence recovery? (Book Chapter, 2025)]
# 10:22 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Grit_and_academic_achievement&amp;diff=prev&amp;oldid=2830325 Changed few sentences to make it grammatically better - For this chapter: Grit and academic achievement  What role does grit play in academic achievement and can it be fostered in future students? (Book Chapter, 2025)]
# 10:48 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830328&amp;oldid=2823381 Rewrote one paragraph in overview section to make it easier to understand - For this chapter: Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake?(Book Chapter, 2025)]
# 10:54 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830330&amp;oldid=2830328 Added reference to support one claim in overview section - For this chapter: Cancer screening and emotion:How do emotions such as fear, anxiety, and relief influence cancer screening uptake? (Book Chapter, 2025)]
#12:56 pm, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261 Commented on discussion forum about what interests me more in motivation and emotion unit and what I would like to learn (UC Learn)]
#9:17 pm, 3 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2830732&amp;oldid=2830326 Corrected grammar and sentence structure, fixed spelling, removed repetition, and improved wording for clarity and flow - For this chapter: Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students? - (Book Chapter, 2025)]
#9:27 pm, 3 September 2026: [[Talk:Motivation and emotion/Book/2026/Outdoor play and children's emotional well-being|Provided suggestion for wikiversity book chapter page and clarified that the user page should be separate than the book chapter - For this chapter: Outdoor play and children's emotional well-being - How does outdoor play influence children's emotional well-being? Overview - (Book Chapter, 2025)]]
#8:28 am, 4 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Commented on discussion forum about what motivates me and what helps me to keep going if I am not feeling motivated (UC Learn)] 
#8:30 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2831894&amp;oldid=2830732 Changed few spelling errors, fixed sentence structure and punctuation, shortened some repetitive wording while keeping original ideas - For this chapter- Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students? - (Book Chapter, 2025)]
#8:50 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2831919&amp;oldid=2830330 Changed few sentences to make it grammatically correct and to maintain sentence flow - For this chapter - Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake? - (Book chapter, 2025)]
#8:34 pm, 8 September 2026:[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FBoredom_and_substance_use&amp;diff=2832227&amp;oldid=2804069 Changed few sentences to make it grammatically correct and added citations to support few claims - For this  chapter - Boredom and substance use: What role does boredom play in motivating substance use?- (Book chapter, 2025)]
#8:43 pm, 8 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FBoredom_and_substance_use&amp;diff=2832228&amp;oldid=2832227 Added citations to support claims in overview section - For this chapter - Boredom and substance use: What role does boredom play in motivating substance use ? (Book chapter, 2025)]
#8:59 pm, 8 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455064 Commented on UC Learn discussion forum to connect with peers and also shared my Linkedln profile]
#9:19 pm, 8 September 2026: [[Talk:Motivation and emotion/Book/2026/Warm-glow giving|Provided suggestion about overview section on talk page - For this chapter - Warm-glow giving - Why does giving feel good and how does this influence prosocial behaviour?- (Book chapter, 2026)]]
#9:43 pm, 8 September 2026: [https://en.wikiversity.org/w/index.php?title=Talk%3AMotivation_and_emotion%2FBook%2F2026%2FSubcortical_structures_and_motivational_drive#See_also_and_external_links_section Commented on talk page to improve see also, external links,  and conclusion section - For this chapter - Subcortical structures and motivational drive: How do subcortical brain regions generate basic motivational impulses and energy?- (Book chapter, 2026)]
#3:07 pm , 9 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2022%2FEnvironmental_volunteering_motivation&amp;diff=2832334&amp;oldid=2814930 Corrected few grammatical errors, added citation to few important claims, provided an introductory paragraph in environmental volunteering section, explained few points in detail, added volume number in one of the references - For this chapter - Environmental volunteering motivation: What motivates environmental volunteering (Book chapter, 2022)]
#3:19 pm, 9 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457190 Commented on UC Learn about a book chapter question related to value congruence and motivation]
#9:35 pm, 9 September 2026: [[Talk:Motivation and emotion/Book/2026/Alcohol use for emotion regulation|Provided suggestion about book chapter that chapter should include both positive and negative dysregulation - For this chapter - Alcohol use for emotion regulation : why and how people use alcohol to regulate their emotions? - (Book chapter, 2026)]]
#9:45 pm, 9 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FAlcohol_use_for_emotion_regulation&amp;diff=2832417&amp;oldid=2830147 Fixed title for this chapter - For this chapter - Alcohol use for emotion regulation: why and how people use alcohol to regulate their emotions? - (Book chapter, 2026)]
#10:00 am, 11 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/461216 Contributed in discussion forum and answered question about word count (UC Learn)]
#10:40 am, 11 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FE-cigarette_use_motivation&amp;diff=2832747&amp;oldid=2754142 Used bullet points to organise see also and external link section and included source in parentheses - For this chapter - E-cigarettes use motivation: What motivates starting and continuing vaping of nicotine e-cigarettes? - (Book chapter, 2024)]
#11:01 am, 11 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FSleep_and_ego_depletion&amp;diff=2832750&amp;oldid=2741278 Corrected grammar and spelling errors - For this chapter - Sleep and ego depletion: How does sleep affect the capacity for self-control and willpower? - (Book chapter, 2024)]
#11:14 pm, 11 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2020%2FChild_killer_motivation&amp;diff=2832817&amp;oldid=2721628 Used bullet points to organise see also section and provided few external sources - For this chapter - Child killer motivation: What motivates a child to kill? (Book chapter, 2020)]
#9:02 pm, 12 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2022%2FBurnout&amp;diff=2832924&amp;oldid=2666399 Fixed overcapitalisation in focus questions, moved one reference into references section and fixed see also section - For this chapter - Burnout: What is burnout and how can be it managed and prevented - (Book chapter, 2022)]
#9:37 pm, 12 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2022%2FTo-do_lists&amp;diff=2832933&amp;oldid=2655448 Corrected grammar and spelling errors - For this chapter -To-do lists: Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - (Book chapter, 2022)]
#8:17 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAbusive_relationships_and_emotional_dependency&amp;diff=2833144&amp;oldid=2723675 Rewrote sentence to make it more clear to understand - For this chapter - Abusive relationships and emotional dependency: What psychological mechanisms drive emotional dependency and how does it perpetuate abusive relationships?(Book chapter, 2024)]
#8:34 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FDopamine_fasting&amp;diff=2833148&amp;oldid=2716222 Rewrote few sentences to make it grammatically correct- For this chapter -Dopamine fasting: What is dopamine fasting and how does it affect motivation and emotion?- (Book chapter, 2024)]
#8:41 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2018%2FBody_image_and_emotional_well-being&amp;diff=2833150&amp;oldid=2596066 Improved see also section - For this chapter - Body image and emotional well-being: How does body image influence one's emotional well being?- (Book chapter, 2018)]
#8:47 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2021%2FClimate_change_helplessness&amp;diff=2833152&amp;oldid=2596067 Corrected few spellings and external links section - For this chapter -Climate change helplessness: How does learned helplessness impact motivation to engage in behaviours to limit climate change?(Book chapter, 2021)]
#9:05 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2021%2FDental_fear&amp;diff=2833154&amp;oldid=2649741 Corrected grammatical errors - For this chapter -Dental fear: What causes dental fear, what are the consequences, and how can it be managed? - (Book chapter, 2021)]
#7:01 pm, 15 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPsychedelic_treatment_of_eating_disorders&amp;diff=2833299&amp;oldid=2832896 Corrected 2 spelling mistake - For this chapter- Psychedelic treatment of eating disorders:] [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPsychedelic_treatment_of_eating_disorders&amp;diff=2833299&amp;oldid=2832896 How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders? - (Book chapter, 2026)] 
#7:14 pm, 15 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FWisdom%2C_motivation%2C_and_emotion&amp;diff=2833301&amp;oldid=2831617 Corrected spelling error - For this  chapter - Wisdom, motivation, and emotion: How do motivational and emotional processes contribute to wisdom? - (Book chapter, 2026)]
#11:05 am, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FGender_and_achievement_motivation&amp;diff=2833381&amp;oldid=2832014 Corrected few grammatical errors - For this Chapter - Gender and achievement motivation: How does gender shape where, how, and under what conditions achievement motivation is expressed? - (Book chapter, 2026)]
#11:23 am, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FVolunteer_wellbeing&amp;diff=2833387&amp;oldid=2829983 Corrected grammar error - For this chapter -Volunteer wellbeing: How does volunteering affect volunteers' subjective wellbeing? - (Book chapter, 2026)]
#7: 38 pm, 16 September 2026: [[Talk:Motivation and emotion/Book/2026/Creative inspiration and effort|Commented on talk page and provided suggestion about theory that can be included in the chapter - For this chapter - Creative inspiration and effort: How do inspiration and effort interact during the creative process?]]
#3:35 pm, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAlcohol%2C_dopamine%2C_motivation%2C_and_emotion&amp;diff=2833572&amp;oldid=2677570 Corrected 2 spellings - For this chapter - Alcohol, dopamine, motivation, and emotion:] [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAlcohol%2C_dopamine%2C_motivation%2C_and_emotion&amp;diff=2833572&amp;oldid=2677570 What role does dopamine play in motivational and emotional responses to alcohol consumption? - (Book chapter, 2024)]
#3:48 pm, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FVasopressin_and_motivation&amp;diff=2833579&amp;oldid=2729665 Corrected spelling error - For this chapter - Vasopressin and motivation: How does vasopressin influence motivation? - (Book chapter, 2024)]
#3:53 pm, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FSleep_onset_optimisation&amp;diff=2833580&amp;oldid=2687478 Corrected 2 spellings - For this chapter - Sleep onset optimisation : What techniques assist in falling asleep promptly? - (Book chapter, 2024)]
#2:12 pm, 18 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FProcrastination_and_temporal_discounting&amp;diff=2833689&amp;oldid=2761864 Corrected spelling errors - Procastination and temporal discounting: How does valuing immediate rewards over future outcomes contribute to procrastination? - (Book chapter, 2025)]
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      <text bytes="17164" sha1="bbzenq31m9z2dcr0jt4psn4qrcdtzco" xml:space="preserve">== About me ==
Hello Everyone,

I am currently a 3rd year psychology student at [https://www.google.com/search?client=safari&amp;rls=en&amp;q=University+of+canberra&amp;ie=UTF-8&amp;oe=UTF-8 University of Canberra] 

This semester I am studying [[Motivation and emotion|Motivation and Emotion]] unit.

My future goal is to become clinical psychologist and work with Australian Federal Police.

My Linkedln profile:  https://www.linkedin.com/in/palak-kathiriya-6b7048289/

Thank you for visiting my linkedln profile and this page!

== Hobbies ==

* Dancing
* Hiking
* Travelling to different countries 
* Painting 
* Cycling 
* Nature exploration
** Birdwatching
** Gardening 

== Book Chapter I'm working on ==
I am working on a really interesting topic for my book chapter. My chapter title is: Positive emotion dysregulation: What is positive emotion dysregulation and how does it affect psychological functioning? 

Link for my book chapter: [[Motivation and emotion/Book/2026/Positive emotion dysregulation|Positive emotion dysregulation]] 

== Social contributions ==
All times are in Canberra local time (AEST/AEDT)
# 12:58 pm, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FWarm-glow_giving&amp;diff=2826658&amp;oldid=2826657 Added the template and the title for this page - For this chapter: Warm-glow giving - Why does giving feel good and how does this influence prosocial behaviour? '''('''Book Chapter, 2026)]
# 11:59 am, 26 August 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPerfectionism_and_procrastination&amp;diff=2826589&amp;oldid=2826579 Fixed spelling error in one of the focus question - For this chapter:  Perfectionism and procrastination - What is the role of perfectionism in procrastination and what can be done about it? (Book Chapter, 2026)]
# 12:28 pm, 26 August 2026: [[Talk:Motivation and emotion/Book/2026/Motivations for using sex work services#Heading casing|Made a suggestion about overview section - For this chapter: Motivations for using sex work services: What motivates use of sex work services? (Book Chapter, 2026)]]
# 2:03 pm, 26 August 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456558 Provided a couple of sources for the development of breathing exercises and relaxation book chapter (Book Chapter, 2026) (UC Learn)]
#8:10 am, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/458145 Commented on discussion forum about how to use GenAI in the unit and what are the expectations if we use GenAI (UC Learn)]
# 10:14 am , 2 September 2026:[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FSelf-control_and_ego_depletion_recovery&amp;diff=2830323&amp;oldid=2761410 Fixed spelling error in book chapter - For this chapter - Self-control and ego depletion recovery: How do people restore self-control resources after depletion and what factors influence recovery? (Book Chapter, 2025)]
# 10:22 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Grit_and_academic_achievement&amp;diff=prev&amp;oldid=2830325 Changed few sentences to make it grammatically better - For this chapter: Grit and academic achievement  What role does grit play in academic achievement and can it be fostered in future students? (Book Chapter, 2025)]
# 10:48 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830328&amp;oldid=2823381 Rewrote one paragraph in overview section to make it easier to understand - For this chapter: Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake?(Book Chapter, 2025)]
# 10:54 am, 2 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2830330&amp;oldid=2830328 Added reference to support one claim in overview section - For this chapter: Cancer screening and emotion:How do emotions such as fear, anxiety, and relief influence cancer screening uptake? (Book Chapter, 2025)]
#12:56 pm, 2 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261 Commented on discussion forum about what interests me more in motivation and emotion unit and what I would like to learn (UC Learn)]
#9:17 pm, 3 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2830732&amp;oldid=2830326 Corrected grammar and sentence structure, fixed spelling, removed repetition, and improved wording for clarity and flow - For this chapter: Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students? - (Book Chapter, 2025)]
#9:27 pm, 3 September 2026: [[Talk:Motivation and emotion/Book/2026/Outdoor play and children's emotional well-being|Provided suggestion for wikiversity book chapter page and clarified that the user page should be separate than the book chapter - For this chapter: Outdoor play and children's emotional well-being - How does outdoor play influence children's emotional well-being? Overview - (Book Chapter, 2025)]]
#8:28 am, 4 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Commented on discussion forum about what motivates me and what helps me to keep going if I am not feeling motivated (UC Learn)] 
#8:30 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FGrit_and_academic_achievement&amp;diff=2831894&amp;oldid=2830732 Changed few spelling errors, fixed sentence structure and punctuation, shortened some repetitive wording while keeping original ideas - For this chapter- Grit and academic achievement - What role does grit play in academic achievement and can it be fostered in future students? - (Book Chapter, 2025)]
#8:50 am, 7 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FCancer_screening_and_emotion&amp;diff=2831919&amp;oldid=2830330 Changed few sentences to make it grammatically correct and to maintain sentence flow - For this chapter - Cancer screening and emotion: How do emotions such as fear, anxiety, and relief influence cancer screening uptake? - (Book chapter, 2025)]
#8:34 pm, 8 September 2026:[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FBoredom_and_substance_use&amp;diff=2832227&amp;oldid=2804069 Changed few sentences to make it grammatically correct and added citations to support few claims - For this  chapter - Boredom and substance use: What role does boredom play in motivating substance use?- (Book chapter, 2025)]
#8:43 pm, 8 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FBoredom_and_substance_use&amp;diff=2832228&amp;oldid=2832227 Added citations to support claims in overview section - For this chapter - Boredom and substance use: What role does boredom play in motivating substance use ? (Book chapter, 2025)]
#8:59 pm, 8 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455064 Commented on UC Learn discussion forum to connect with peers and also shared my Linkedln profile]
#9:19 pm, 8 September 2026: [[Talk:Motivation and emotion/Book/2026/Warm-glow giving|Provided suggestion about overview section on talk page - For this chapter - Warm-glow giving - Why does giving feel good and how does this influence prosocial behaviour?- (Book chapter, 2026)]]
#9:43 pm, 8 September 2026: [https://en.wikiversity.org/w/index.php?title=Talk%3AMotivation_and_emotion%2FBook%2F2026%2FSubcortical_structures_and_motivational_drive#See_also_and_external_links_section Commented on talk page to improve see also, external links,  and conclusion section - For this chapter - Subcortical structures and motivational drive: How do subcortical brain regions generate basic motivational impulses and energy?- (Book chapter, 2026)]
#3:07 pm , 9 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2022%2FEnvironmental_volunteering_motivation&amp;diff=2832334&amp;oldid=2814930 Corrected few grammatical errors, added citation to few important claims, provided an introductory paragraph in environmental volunteering section, explained few points in detail, added volume number in one of the references - For this chapter - Environmental volunteering motivation: What motivates environmental volunteering (Book chapter, 2022)]
#3:19 pm, 9 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457190 Commented on UC Learn about a book chapter question related to value congruence and motivation]
#9:35 pm, 9 September 2026: [[Talk:Motivation and emotion/Book/2026/Alcohol use for emotion regulation|Provided suggestion about book chapter that chapter should include both positive and negative dysregulation - For this chapter - Alcohol use for emotion regulation : why and how people use alcohol to regulate their emotions? - (Book chapter, 2026)]]
#9:45 pm, 9 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FAlcohol_use_for_emotion_regulation&amp;diff=2832417&amp;oldid=2830147 Fixed title for this chapter - For this chapter - Alcohol use for emotion regulation: why and how people use alcohol to regulate their emotions? - (Book chapter, 2026)]
#10:00 am, 11 September 2026: [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/461216 Contributed in discussion forum and answered question about word count (UC Learn)]
#10:40 am, 11 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FE-cigarette_use_motivation&amp;diff=2832747&amp;oldid=2754142 Used bullet points to organise see also and external link section and included source in parentheses - For this chapter - E-cigarettes use motivation: What motivates starting and continuing vaping of nicotine e-cigarettes? - (Book chapter, 2024)]
#11:01 am, 11 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FSleep_and_ego_depletion&amp;diff=2832750&amp;oldid=2741278 Corrected grammar and spelling errors - For this chapter - Sleep and ego depletion: How does sleep affect the capacity for self-control and willpower? - (Book chapter, 2024)]
#11:14 pm, 11 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2020%2FChild_killer_motivation&amp;diff=2832817&amp;oldid=2721628 Used bullet points to organise see also section and provided few external sources - For this chapter - Child killer motivation: What motivates a child to kill? (Book chapter, 2020)]
#9:02 pm, 12 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2022%2FBurnout&amp;diff=2832924&amp;oldid=2666399 Fixed overcapitalisation in focus questions, moved one reference into references section and fixed see also section - For this chapter - Burnout: What is burnout and how can be it managed and prevented - (Book chapter, 2022)]
#9:37 pm, 12 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2022%2FTo-do_lists&amp;diff=2832933&amp;oldid=2655448 Corrected grammar and spelling errors - For this chapter -To-do lists: Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - (Book chapter, 2022)]
#8:17 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAbusive_relationships_and_emotional_dependency&amp;diff=2833144&amp;oldid=2723675 Rewrote sentence to make it more clear to understand - For this chapter - Abusive relationships and emotional dependency: What psychological mechanisms drive emotional dependency and how does it perpetuate abusive relationships?(Book chapter, 2024)]
#8:34 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FDopamine_fasting&amp;diff=2833148&amp;oldid=2716222 Rewrote few sentences to make it grammatically correct- For this chapter -Dopamine fasting: What is dopamine fasting and how does it affect motivation and emotion?- (Book chapter, 2024)]
#8:41 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2018%2FBody_image_and_emotional_well-being&amp;diff=2833150&amp;oldid=2596066 Improved see also section - For this chapter - Body image and emotional well-being: How does body image influence one's emotional well being?- (Book chapter, 2018)]
#8:47 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2021%2FClimate_change_helplessness&amp;diff=2833152&amp;oldid=2596067 Corrected few spellings and external links section - For this chapter -Climate change helplessness: How does learned helplessness impact motivation to engage in behaviours to limit climate change?(Book chapter, 2021)]
#9:05 pm, 14 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2021%2FDental_fear&amp;diff=2833154&amp;oldid=2649741 Corrected grammatical errors - For this chapter -Dental fear: What causes dental fear, what are the consequences, and how can it be managed? - (Book chapter, 2021)]
#7:01 pm, 15 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPsychedelic_treatment_of_eating_disorders&amp;diff=2833299&amp;oldid=2832896 Corrected 2 spelling mistake - For this chapter- Psychedelic treatment of eating disorders:] [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FPsychedelic_treatment_of_eating_disorders&amp;diff=2833299&amp;oldid=2832896 How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders? - (Book chapter, 2026)] 
#7:14 pm, 15 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FWisdom%2C_motivation%2C_and_emotion&amp;diff=2833301&amp;oldid=2831617 Corrected spelling error - For this  chapter - Wisdom, motivation, and emotion: How do motivational and emotional processes contribute to wisdom? - (Book chapter, 2026)]
#11:05 am, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FGender_and_achievement_motivation&amp;diff=2833381&amp;oldid=2832014 Corrected few grammatical errors - For this Chapter - Gender and achievement motivation: How does gender shape where, how, and under what conditions achievement motivation is expressed? - (Book chapter, 2026)]
#11:23 am, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FVolunteer_wellbeing&amp;diff=2833387&amp;oldid=2829983 Corrected grammar error - For this chapter -Volunteer wellbeing: How does volunteering affect volunteers' subjective wellbeing? - (Book chapter, 2026)]
#7: 38 pm, 16 September 2026: [[Talk:Motivation and emotion/Book/2026/Creative inspiration and effort|Commented on talk page and provided suggestion about theory that can be included in the chapter - For this chapter - Creative inspiration and effort: How do inspiration and effort interact during the creative process?]]
#3:35 pm, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAlcohol%2C_dopamine%2C_motivation%2C_and_emotion&amp;diff=2833572&amp;oldid=2677570 Corrected 2 spellings - For this chapter - Alcohol, dopamine, motivation, and emotion:] [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAlcohol%2C_dopamine%2C_motivation%2C_and_emotion&amp;diff=2833572&amp;oldid=2677570 What role does dopamine play in motivational and emotional responses to alcohol consumption? - (Book chapter, 2024)]
#3:48 pm, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FVasopressin_and_motivation&amp;diff=2833579&amp;oldid=2729665 Corrected spelling error - For this chapter - Vasopressin and motivation: How does vasopressin influence motivation? - (Book chapter, 2024)]
#3:53 pm, 16 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FSleep_onset_optimisation&amp;diff=2833580&amp;oldid=2687478 Corrected 2 spellings - For this chapter - Sleep onset optimisation : What techniques assist in falling asleep promptly? - (Book chapter, 2024)]
#2:12 pm, 18 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FProcrastination_and_temporal_discounting&amp;diff=2833689&amp;oldid=2761864 Corrected spelling errors - Procastination and temporal discounting: How does valuing immediate rewards over future outcomes contribute to procrastination? - (Book chapter, 2025)]
#2:20 pm, 18 September 2026: [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FMaladaptive_defence_mechanisms_and_distress&amp;diff=2833691&amp;oldid=2761577 Corrected spelling errors - Maladaptive defence mechanisms and distress: In what ways do maladaptive defences shape emotional regulation and behavioural responses when under pressure? - (Book chapter, 2025)]</text>
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    <title>Wikiversity:Candidates for Interface Adminship/Codename Noreste</title>
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      <timestamp>2026-09-18T07:30:31Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <comment>/* Comments/questions */ reply ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
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      <text bytes="2785" sha1="2dpg3y41rucd8p34ayz6891wi5j4cmf" xml:space="preserve">=== {{user|Codename Noreste}} ===
&lt;!-- State your reasoning below on why you are requesting any permission. Do not add your signature, as it will be automatically added for you. --&gt;
Hello, everyone. Although it is not mentioned by the interface administrator policy, I would like to run for permanent interface administrator permissions (since my temporary IA rights are about to expire). My original stated reasoning was because of the ability to adjust interface pages for dark mode support and to adjust the CSS. However, I am familiar with CSS and I would like to be the first permanent interface administrator on English Wikiversity (to perform technical maintenance). See also [[Wikiversity:Colloquium#Wikiversity talk:Interface administrators#My thoughts about this user group|this discussion]] for context.

I already have 2FA enabled as I hold IA rights on several other projects. Thank you for your consideration. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 16:53, 7 September 2026 (UTC)
: I think we would first need a change to policy which currently only allows for 14 to 120 day IA periods.
: Could you summarise recent changes you've made to the en.wv interface?
: And what future changes are you planning on making to the en.wv interface? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:54, 7 September 2026 (UTC)
:: When I became an interface administrator (prior to being a custodian), I edited several interface messages to adjust for dark mode support. I initially planned to edit the CSS page by removing outdated code and moving the CSS import code (&lt;code&gt;@import url&lt;/code&gt;) to common.css itself, but I didn't have time to do that due to commitments in real life and in other projects. Now that I have that time here, I am willing to perform maintenance on CSS. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 13:43, 8 September 2026 (UTC)
::: I forgot to mention this, but since I proposed an amendment to the IA policy, another maximum extension would be fine. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 13:44, 8 September 2026 (UTC)

==== Comments/questions ====
: It has been roughly more than a week, can this request be closed? Thank you. [[User:Codename Noreste|&lt;span style=&quot;color: blue&quot;&gt;Codename Noreste&lt;/span&gt;]] /// [[User talk:Codename Noreste|⭐️✨]] 07:30, 18 September 2026 (UTC)

==== Votes ====
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:20, 14 September 2026 (UTC)</text>
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  <page>
    <title>Plant Divisions (Phyla)/Magnoliophyta</title>
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        <username>The Citer</username>
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      <comment>Added another reference.</comment>
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      <text bytes="6342" sha1="b3kbfaph2wifxiykfy4ci220wz9feqt" xml:space="preserve">[[Image:Tree of Angiosperm Phylogeny 2024.jpg|thumb|300px|right|Many species of Angiospermae phylogenetic picture.]]
Flowering plants are plants that bear flowers and fruits, and form the clade Angiospermae (/ˌændʒiəˈspɜːrmiː/). The term ''angiosperm'' is derived from the Greek words ἀγγεῖον (angeion; 'container, vessel') and σπέρμα (sperma; 'seed'), meaning that the seeds are enclosed within a fruit. The group was formerly called Magnoliophyta. Angiosperms are by far the most diverse group of land plants with 64 orders, 416 families, approximately 13,000 known genera and 300,000 known species! The diversity of flowering plants is not evenly distributed. Nearly all species belong to the eudicot (75%), monocot (23%), and magnoliid (2%) clades. The remaining five clades contain a little over 250 species in total; i.e. less than 0.1% of flowering plant diversity, divided among nine families. The 25 most speciated families are:
{| class=&quot;wikitable sortable&quot;
|+ The 25 largest angiosperm families
|-
! &lt;!--Rank, by size--&gt; !! Group !! Family !! English name !! No. of spp. 
|-
| 1 || Eudicot ||  Asteraceae or Compositae  || daisy ||  22,750 
|-
| 2 || Monocot ||  Orchidaceae  || orchid ||  21,950 
|-
| 3 || Eudicot ||  Fabaceae or Leguminosae  || pea, legume ||  19,400 
|-
| 4 || Eudicot ||  Rubiaceae  || Rubia|madder ||  13,150&lt;ref&gt;{{cite web|title=Kew Scientist 30|date=October 2006|url=https://www.kew.org/kewscientist/ks_30.pdf|archive-url=https://web.archive.org/web/20070927005410/https://www.kew.org/kewscientist/ks_30.pdf|archive-date=27 September 2007}}&lt;/ref&gt;
|-
| 5 || Monocot ||  Poaceae or Gramineae  || grass ||  10,035 
|-
| 6 || Eudicot ||  Lamiaceae or Labiatae  || mint ||  7,175 
|-
| 7 || Eudicot ||  Euphorbiaceae  || spurge ||  5,735 
|-
| 8 || Eudicot ||  Melastomataceae  || melastome ||  5,005 
|-
| 9 || Eudicot ||  Myrtaceae || myrtle ||  4,625 
|-
| 10 || Eudicot ||  Apocynaceae  || dogbane ||  4,555 
|-
| 11 || Monocot ||  Cyperaceae  || sedge ||  4,350 
|-
| 12 || Eudicot ||  Malvaceae  || mallow ||  4,225 
|-
| 13 || Monocot ||  Araceae  || arum ||  4,025 
|-
| 14 || Eudicot ||  Ericaceae  || heath ||  3,995 
|-
| 15 || Eudicot ||  Gesneriaceae  || gesneriad ||  3,870 
|-
| 16 || Eudicot ||  Apiaceae or Umbelliferae  || parsley ||  3,780 
|-
| 17 || Eudicot ||  Brassicaceae or Cruciferae  || cabbage ||  3,710
|-
| 18 || Magnoliid dicot ||  Piperaceae  || pepper ||  3,600 
|-
| 19 || Monocot ||  Bromeliaceae  || bromeliad ||  3,540 
|-
| 20 || Eudicot ||  Acanthaceae  || acanthus ||  3,500 
|-
| 21 || Eudicot ||  Rosaceae  || rose ||  2,830 
|-
| 22 || Eudicot ||  Boraginaceae  || borage ||  2,740 
|-
| 23 || Eudicot ||  Urticaceae  || nettle ||  2,625 
|-
| 24 || Eudicot ||  Ranunculaceae  || buttercup ||  2,525 
|-
| 25 || Magnoliid dicot ||  Lauraceae  || laurel ||  2,500 
|}
==More facts==
===Name Meaning===
Magnolia-like plant

===Major distinguishing characteristics===
Flowers and fruit, vascular system with vessels
==Evolutionary history==
Fossilised spores suggest that embryophytes have existed for at least 475 million years&lt;ref&gt;{{cite journal |last=Edwards |first=D. |title=The role of mid-palaeozoic mesofossils in the detection of early bryophytes |journal=Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences |volume=355 |issue=1398 |pages=733–54; discussion 754–5 |date=June 2000 |pmid=10905607 |pmc=1692787 |doi=10.1098/rstb.2000.0613 }}&lt;/ref&gt; However, angiosperms appeared suddenly and rapidly diversified during the Valanginian (beginning ~130 mya), much later than other major plant groups.&lt;ref&gt;{{Cite journal |last1=Herendeen |first1=Patrick S. |last2=Friis |first2=Else Marie |last3=Pedersen |first3=Kaj Raunsgaard |last4=Crane |first4=Peter R. |date=2017-03-03 |title=Palaeobotanical redux: revisiting the age of the angiosperms |url=https://rdcu.be/c0Zhm |journal=Nature Plants |volume=3 |issue=3 |page=17015 |doi=10.1038/nplants.2017.15 |pmid=28260783 |bibcode=2017NatPl...317015H |s2cid=205458714 |issn=2055-0278}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal |last=Friedman |first=William E. |date=January 2009 |title=The meaning of Darwin's &quot;abominable mystery&quot; |url=https://onlinelibrary.wiley.com/doi/10.3732/ajb.0800150 |journal=American Journal of Botany |volume=96 |issue=1 |pages=5–21 |doi=10.3732/ajb.0800150 |pmid=21628174|bibcode=2009AmJB...96....5F |url-access=subscription }}&lt;/ref&gt; The evolutionary success and rapid diversification of angiosperms are largely attributed to their coevolutionary relationships with animal pollinators, particularly insects, birds, and bats. Unlike [https://en.wikipedia.org/wiki/Gymnosperm gymnosperms], which today rely on wind for pollen dispersal, angiosperms developed specialized traits—such as nectar production, vivid pigmentations, and complex volatile scents—to attract specific floral visitors. 
==Classes==
No one really knows how to divide Angiospermae in to classes. (See [[Talk:Plant Divisions (Phyla)/Magnoliophyta|talk]]) However, we can still list the defined orders.
===Orders===
Acorales – Alismatales – Amborellales – Apiales – Aquifoliales – Arecales – Asparagales – Asterales – Austrobaileyales – Berberidopsidales – Boraginales – Brassicales – Bruniales – Buxales – Canellales – Caryophyllales – Celastrales – Ceratophyllales – Chloranthales – Commelinales – Cornales – Crossosomatales – Cucurbitales – Dilleniales – Dioscoreales – Dipsacales – Ericales – Escalloniales – Fabales – Fagales – Garryales – Gentianales – Geraniales – Gunnerales – Huerteales – Icacinales – Lamiales – Laurales – Liliales – Magnoliales – Malpighiales – Malvales – Metteniusales – Myrtales – Nymphaeales – Oxalidales – Pandanales – Paracryphiales – Petrosaviales – Picramniales – Piperales – Poales – Proteales – Ranunculales – Rosales – Santalales – Sapindales – Saxifragales – Solanales – Trochodendrales – Vahliales – Vitales – Zingiberales – Zygophyllales{{sfnp|ps=none|APG IV|2016|p=5}}

==Quiz==
[[Plant Divisions (Phyla)/Magnoliophyta/Quiz]]
==References==
[[Wikipedia:Flowering plant]]&lt;br&gt;
[[Wikispecies:Magnoliopsida]]
[[Category:Plants]]
[[Category:Taxonomy]]
[[Category:Botany]]
[[Category:Biology]]
[[Category:Flowers]]</text>
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    <title>Talk:Plant Divisions (Phyla)/Magnoliophyta</title>
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      <comment>/* Can we divide Magnoliophyta into usable classes? */ Reply</comment>
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      <text bytes="655" sha1="ogup9q7swcs6tm6us8m7opvyv16mlzo" xml:space="preserve">== Can we divide Magnoliophyta into usable classes? ==
[[User:The Citer|The Citer]] ([[User talk:The Citer|discuss]] • [[Special:Contributions/The Citer|contribs]]) 10:38, 11 September 2026 (UTC)

:We could Put ''Amborella'' into its own class (Amborellaopsida), we could also put Nymphaeales into its own class (Nymphaeaopsida), we could also put Austrobaileyales into its own class (Austrobaileyaopsida), and we could even have Core Angiosperms have its own class (Mesangiospermopsida or Mesomagnolioopsida). [[User:The Citer|The Citer]] ([[User talk:The Citer|discuss]] • [[Special:Contributions/The Citer|contribs]]) 20:21, 17 September 2026 (UTC)</text>
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        <username>The Citer</username>
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      <text bytes="511" sha1="7sql9svzdl120lz5f45bzhnpejk5b1b" xml:space="preserve">== Can we divide Magnoliophyta into usable classes? ==
:We could Put ''Amborella'' into its own class (Amborellaopsida), we could also put Nymphaeales into its own class (Nymphaeaopsida), we could also put Austrobaileyales into its own class (Austrobaileyaopsida), and we could even have Core Angiosperms have its own class (Mesangiospermopsida or Mesomagnolioopsida). [[User:The Citer|The Citer]] ([[User talk:The Citer|discuss]] • [[Special:Contributions/The Citer|contribs]]) 20:21, 17 September 2026 (UTC)</text>
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      <comment>advert1 ([[m:User:ZbVl/VD|Vandoom]])</comment>
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== 2026-09-17 ==
&lt;div class=&quot;mw-content-ltr&quot; dir=&quot;ltr&quot; style=&quot;text-align: left&quot; lang=&quot;en&quot;&gt;[[File:Information.svg|25px|alt=Information icon]] Hello. Apologies for writing this in English, but I wanted to let you know that one or more of [[Special:Contributions/Poonamsharma144|your recent contributions]] have been undone because they appeared to be promotional. [[:m:en:WP:SOAPBOX|Advertising or using &lt;span style=&quot;white-space:nowrap&quot;&gt;Wikiversity&lt;/span&gt; as a &quot;soapbox&quot;]] are not permitted. Take a look at the welcome pages to learn more about &lt;span style=&quot;white-space:nowrap&quot;&gt;Wikiversity&lt;/span&gt;. Thanks. &lt;/div&gt;&lt;!-- Glow-advert1 @ 1789651056023.4s --&gt;&lt;nowiki&gt;&lt;/nowiki&gt; [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:17, 17 September 2026 (UTC)</text>
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    <revision>
      <id>2833626</id>
      <timestamp>2026-09-17T16:37:26Z</timestamp>
      <contributor>
        <username>Huuuuusssssss</username>
        <id>3111191</id>
      </contributor>
      <comment>Created page with &quot;= Cristiano Ronaldo dos Santos Aveiro =  == Biogràfia == Cristiano Ronaldo dos Santos Aveiro, va néixer el 5 de febrer de 1985 a Funchal, Portugal. Des de jove va mostrar una passió pel futbol, jugant amb el club local Andorinha i després al Sporting CP, on va destacar.  El 2003, amb només 18 anys, va fitxar pel Manchester United, on va guanyar el seu primer Ballon d'Or el 2008 i va ajudar l'equip a guanyar la Lliga de Campions. El 2009, es va traslladar al Real Mad...&quot;</comment>
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      <text bytes="1365" sha1="t87e9j7q9zwjapnmod4eolh8ne8gvwh" xml:space="preserve">= Cristiano Ronaldo dos Santos Aveiro =

== Biogràfia ==
Cristiano Ronaldo dos Santos Aveiro, va néixer el 5 de febrer de 1985 a Funchal, Portugal. Des de jove va mostrar una passió pel futbol, jugant amb el club local Andorinha i després al Sporting CP, on va destacar.

El 2003, amb només 18 anys, va fitxar pel Manchester United, on va guanyar el seu primer Ballon d'Or el 2008 i va ajudar l'equip a guanyar la Lliga de Campions. El 2009, es va traslladar al Real Madrid, on va establir-se com un dels millors jugadors de la història, guanyant quatre Lligues de Campions més, cinc Ballons d'Or i trencant rècords de gols.

El 2018, va marxar a la Juventus italiana, on va continuar la seva racha de èxits, guanyant dues Sèrie A i convertint-se en el màxim golejador de la història de la competició. El 2021, va tornar al Manchester United, i el 2022 es va unir a l'Al-Nassr de l'Aràbia Saudita.

En l'àmbit internacional, Ronaldo és el màxim golejador de la història de la selecció portuguesa i un pilar fonamental en les seves victòries, incloent-hi l'Eurocopa de 2016 i la Lliga de Nacions de 2019. És conegut per la seva disciplina ferotge, el seu sentit de la responsabilitat i la seva motivació constant per superar-se.

Amb més de 850 gols en partits oficials, CR7 és un símbol de dedicació i excel·lència en el món del futbol.</text>
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    <revision>
      <id>2833628</id>
      <parentid>2833626</parentid>
      <timestamp>2026-09-17T16:44:53Z</timestamp>
      <contributor>
        <username>Huuuuusssssss</username>
        <id>3111191</id>
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      <text bytes="1390" sha1="1vucooq69uz8brt9by7k05dr5p48719" xml:space="preserve">= '''Cristiano Ronaldo''' dos Santos Aveiro =

== Biogràfia ==
Cristiano Ronaldo dos Santos Aveiro, va néixer el 5 de febrer de 1985 a Funchal, Portugal. Des de jove va mostrar una passió pel futbol, jugant amb el club local Andorinha i després al Sporting CP, on va destacar per la velocitat...

El 2003, amb només 18 anys, va fitxar pel Manchester United, on va guanyar el seu primer Ballon d'Or el 2008 i va ajudar l'equip a guanyar la Lliga de Campions. El 2009, es va traslladar al Real Madrid, on va establir-se com un dels millors jugadors de la història, guanyant quatre Lligues de Campions més, cinc Ballons d'Or i trencant rècords de gols.

El 2018, va marxar a la Juventus italiana, on va continuar la seva racha de èxits, guanyant dues Sèrie A i convertint-se en el màxim golejador de la història de la competició. El 2021, va tornar al Manchester United, i el 2022 es va unir a l'Al-Nassr de l'Aràbia Saudita.

En l'àmbit internacional, Ronaldo és el màxim golejador de la història de la selecció portuguesa i un pilar fonamental en les seves victòries, incloent-hi l'Eurocopa de 2016 i la Lliga de Nacions de 2019. És conegut per la seva disciplina ferotge, el seu sentit de la responsabilitat i la seva motivació constant per superar-se.

Amb més de 850 gols en partits oficials, CR7 és un símbol de dedicació i excel·lència en el món del futbol.</text>
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  <page>
    <title>User:Sedou Sylla/sandbox</title>
    <ns>2</ns>
    <id>332115</id>
    <revision>
      <id>2833627</id>
      <timestamp>2026-09-17T16:44:32Z</timestamp>
      <contributor>
        <username>Sedou Sylla</username>
        <id>3111190</id>
      </contributor>
      <comment>Created page with &quot;=                                '''Biografía Zohran Kwame Mamdani''' = '''Zohran Kwame Mamdani''' (nascut el 18 d'octubre de 1991 a Kampala, Uganda) és un polític i activista nord-americà que és l'&lt;nowiki/&gt;'''alcalde de la ciutat de Nova York''', després d'haver assumit el càrrec l'1 de gener de 2026. Membre de l'ala dels Socialistes Democràtics d'Amèrica (DSA) dins del Partit Demòcrata, va fer història a les eleccions del novembre de 2025 en convertir-se en...&quot;</comment>
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      <text bytes="3627" sha1="pa70ovd03y4c6yuaugcyc29y36fs3bt" xml:space="preserve">=                                '''Biografía Zohran Kwame Mamdani''' =
'''Zohran Kwame Mamdani''' (nascut el 18 d'octubre de 1991 a Kampala, Uganda) és un polític i activista nord-americà que és l'&lt;nowiki/&gt;'''alcalde de la ciutat de Nova York''', després d'haver assumit el càrrec l'1 de gener de 2026. Membre de l'ala dels Socialistes Democràtics d'Amèrica (DSA) dins del Partit Demòcrata, va fer història a les eleccions del novembre de 2025 en convertir-se en el '''primer alcalde musulmà, d'origen sud-asiàtic i el primer ''millennial''''' a governar la ciutat de Nova York.

== '''Vida primerenca i educació''' ==

* '''Orígens familiars:''' És fill d'una coneguda família d'intel·lectuals i artistes. El seu pare és l'acadèmic i especialista en estudis africans indo-ugandès Mahmood Mamdani, i la seva mare és la cèlebre directora de cinema índia Mira Nair. 
* '''Infància i migració:''' Nascut a Uganda, va viure un temps a Ciutat del Cap (Sud-àfrica) abans de traslladar-se amb la seva família a Nova York a l'edat de 7 anys. Va obtenir la nacionalitat nord-americana l'any 2018. 
* '''Estudis:''' Es va graduar a la prestigiosa ''The Bronx High School of Science'' i posteriorment va obtenir una llicenciatura en Estudis Africans al ''Bowdoin College'' de Maine el 2014. 

== '''Trajectòria professional i primers passos en política''' ==
Abans de dedicar-se plenament a la política institucional, Mamdani va treballar com a '''assessor i conseller d'habitatge''' a Nova York, ajudant famílies de baixos ingressos a evitar desnonaments. Al mateix temps, va tenir una faceta artística com a '''raper i músic de hip-hop'''.

La seva transició a la política es va iniciar actuant com a director de campanya per a candidats locals d'esquerres. L'any 2020, va fer el salt com a candidat i va guanyar un escó a l''''Assemblea de l'Estat de Nova York''' en representació del districte 36 (que inclou els barris d'Astoria i Long Island City, a Queens), derrotant a les primàries demòcrates una congressista amb molts anys de trajectòria. Va ser reelegit en el seu lloc legislatiu el 2022 i el 2024. 

== '''L'històric ascens a l'Alcaldia de Nova York''' ==
A finals de 2024, enmig de la crisi política provocada per les investigacions judicials al llavors alcalde Eric Adams, Mamdani va llançar la seva candidatura a l'alcaldia.

Amb una campanya molt focalitzada en les xarxes socials i amb el suport d'un exèrcit de '''més de 100.000 voluntaris''', va aconseguir guanyar primer les primàries demòcrates davant de figures consolidades del partit com l'exgovernador Andrew Cuomo, i posteriorment imposar-se de manera contundent a les eleccions del '''4 de novembre de 2025'''. 

== '''Eixos del seu programa polític''' ==
Mamdani va estructurar el seu programa al voltant de la justícia social i l'assequibilitat de la vida urbana amb propostes com: 

* '''Transport públic:''' Implementació d'autobusos urbans gratuïts a tota la ciutat.
* '''Habitatge:''' Congelació dels lloguers en habitatges protegits i multiplicació de la construcció d'habitatge assequible executada per treballadors sindicats.
* '''Educació i serveis:''' Cuidado infantil i escoles bressol públiques de caràcter universal i gratuït.
* '''Alimentació:''' Creació d'una xarxa de supermercats de gestió municipal amb preus regulats.
* '''Fiscalitat:''' Increment d'impostos a les grans corporacions i a les rendes superiors al milió de dòlars per finançar els serveis públics.

== '''Vida personal''' ==
Està casat amb '''Rama Duwaji''', una artista d'origen sirià resident a Brooklyn.</text>
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  <page>
    <title>User:JonAwbrey/Figures and Tables 57</title>
    <ns>2</ns>
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    <revision>
      <id>2833629</id>
      <timestamp>2026-09-17T16:54:18Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <comment>add user work page + &lt;h2&gt;Minimal Negation Operators&lt;/h2&gt;</comment>
      <origin>2833629</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="35" sha1="f49pf1wc7v50hd1xat00w995q9fl3qa" xml:space="preserve">&lt;h2&gt;Minimal Negation Operators&lt;/h2&gt;</text>
      <sha1>f49pf1wc7v50hd1xat00w995q9fl3qa</sha1>
    </revision>
    <revision>
      <id>2833631</id>
      <parentid>2833629</parentid>
      <timestamp>2026-09-17T17:02:10Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <origin>2833631</origin>
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      <text bytes="107" sha1="m7tts4moa06u4lhhtaff3j8tczhtjop" xml:space="preserve">&lt;h2&gt;Minimal Negation Operators 0, 1, 2, 3 Arguments&lt;/h2&gt;

&lt;h3&gt;LaTeX 1&lt;h3&gt;

&lt;h3&gt;LaTeX 2&lt;h3&gt;

&lt;h3&gt;LaTeX 3&lt;h3&gt;</text>
      <sha1>m7tts4moa06u4lhhtaff3j8tczhtjop</sha1>
    </revision>
    <revision>
      <id>2833633</id>
      <parentid>2833631</parentid>
      <timestamp>2026-09-17T17:04:31Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <origin>2833633</origin>
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      <text bytes="624" sha1="qppr3snmyxhieflfps2f0vsf1p68bxt" xml:space="preserve">&lt;h2&gt;Minimal Negation Operators 0, 1, 2, 3 Arguments&lt;/h2&gt;

&lt;h3&gt;LaTeX Variant 3&lt;h3&gt;

&lt;h3&gt;LaTeX Variant 2&lt;h3&gt;

&lt;h3&gt;LaTeX Variant 1&lt;h3&gt;

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(x)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x^\prime
\\[6pt]
\texttt{(x, y)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x^\prime y \lor x y^\prime
\\[6pt]
\texttt{(x, y, z)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x^\prime y z \lor x y^\prime z \lor x y z^\prime
\end{matrix}&lt;/math&gt;
|}</text>
      <sha1>qppr3snmyxhieflfps2f0vsf1p68bxt</sha1>
    </revision>
    <revision>
      <id>2833635</id>
      <parentid>2833633</parentid>
      <timestamp>2026-09-17T17:10:09Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <comment>==Minimal Negation Operators 0, 1, 2, 3 Arguments== (don't use &lt;h2&gt;...&lt;/h2&gt; etc. here)</comment>
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      <text bytes="613" sha1="prassmaqy986vige18es6wbii09vri3" xml:space="preserve">==Minimal Negation Operators 0, 1, 2, 3 Arguments==

===LaTeX Variant 3===

===LaTeX Variant 2===

===LaTeX Variant 1===

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(x)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x^\prime
\\[6pt]
\texttt{(x, y)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x^\prime y \lor x y^\prime
\\[6pt]
\texttt{(x, y, z)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x^\prime y z \lor x y^\prime z \lor x y z^\prime
\end{matrix}&lt;/math&gt;
|}</text>
      <sha1>prassmaqy986vige18es6wbii09vri3</sha1>
    </revision>
    <revision>
      <id>2833636</id>
      <parentid>2833635</parentid>
      <timestamp>2026-09-17T17:20:03Z</timestamp>
      <contributor>
        <username>JonAwbrey</username>
        <id>29537</id>
      </contributor>
      <comment>/* Minimal Negation Operators 0, 1, 2, 3 Arguments */</comment>
      <origin>2833636</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1734" sha1="a3zrpc4zx65zvqrix5303hqj8w6fc8p" xml:space="preserve">==Minimal Negation Operators 0, 1, 2, 3 Arguments==

===LaTeX Variant 3===

Uses \prime + \texttt{(} x \texttt{,} y \texttt{)} etc.

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(} x \texttt{)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x\prime
\\[6pt]
\texttt{(} x \texttt{,} y \texttt{)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x\prime y \lor x y\prime
\\[6pt]
\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x\prime y z \lor x y\prime z \lor x y z\prime
\end{matrix}&lt;/math&gt;
|}

===LaTeX Variant 2===

Uses \prime

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(x)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x\prime
\\[6pt]
\texttt{(x, y)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x\prime y \lor x y\prime
\\[6pt]
\texttt{(x, y, z)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x\prime y z \lor x y\prime z \lor x y z\prime
\end{matrix}&lt;/math&gt;
|}

===LaTeX Variant 1===

Uses ^\prime

{| align=&quot;center&quot; cellpadding=&quot;4&quot; style=&quot;text-align:center&quot;
|
&lt;math&gt;\begin{matrix}
\texttt{()}
&amp; = &amp; \nu_0
&amp; = &amp; 0
&amp; = &amp; \mathrm{false}
\\[6pt]
\texttt{(x)}
&amp; = &amp; \nu_1 (x)
&amp; = &amp; \tilde{x}
&amp; = &amp; x^\prime
\\[6pt]
\texttt{(x, y)}
&amp; = &amp; \nu_2 (x, y)
&amp; = &amp; \tilde{x}y \lor x\tilde{y}
&amp; = &amp; x^\prime y \lor x y^\prime
\\[6pt]
\texttt{(x, y, z)}
&amp; = &amp; \nu_3 (x, y, z)
&amp; = &amp; \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
&amp; = &amp; x^\prime y z \lor x y^\prime z \lor x y z^\prime
\end{matrix}&lt;/math&gt;
|}</text>
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  <page>
    <title>User:Gabipc3/sandbox</title>
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      <comment>Created page with &quot;== PRESENTACIÓ PERSONAL == Hola! Em dic '''Gabi''' i tinc 21 anys i soc estudiant de '''DAW.'''  == FORMACIÓ == He estudiat cuina i pastisseria. Actualment estic estudiant Desenvolupament d'Aplicacions Web.  == AFICIONS == &lt;nowiki&gt;*&lt;/nowiki&gt; Jugar a videojocs * Jugar a escacs * Escoltar música * Llegir manga*   ░░░░░░░▄██▄░░░░░░▄▄░░  ░░░░░░░▐███▀░░░░░▄███▌  ░░▄▀░░▄█...&quot;</comment>
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      <text bytes="1127" sha1="4io9a18k8x13d8y9mop39m5a3brz7dh" xml:space="preserve">== PRESENTACIÓ PERSONAL ==
Hola! Em dic '''Gabi''' i tinc 21 anys i soc estudiant de '''DAW.'''

== FORMACIÓ ==
He estudiat cuina i pastisseria. Actualment estic estudiant Desenvolupament d'Aplicacions Web.

== AFICIONS ==
&lt;nowiki&gt;*&lt;/nowiki&gt; Jugar a videojocs * Jugar a escacs * Escoltar música * Llegir manga*


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    <revision>
      <id>2833632</id>
      <parentid>2833630</parentid>
      <timestamp>2026-09-17T17:02:29Z</timestamp>
      <contributor>
        <username>Gabipc3</username>
        <id>3111198</id>
      </contributor>
      <comment>/* AFICIONS */</comment>
      <origin>2833632</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1126" sha1="5q6b2u4v7u07e7uyz2uyu5yxxb1pn0w" xml:space="preserve">== PRESENTACIÓ PERSONAL ==
Hola! Em dic '''Gabi''' i tinc 21 anys i soc estudiant de '''DAW.'''

== FORMACIÓ ==
He estudiat cuina i pastisseria. Actualment estic estudiant Desenvolupament d'Aplicacions Web.

== AFICIONS ==
&lt;nowiki&gt;*&lt;/nowiki&gt; Jugar a videojocs * Jugar a escacs * Escoltar música * Llegir manga


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        <username>Gabipc3</username>
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      <text bytes="1112" sha1="rlvhc6938w6bw2d2p043tw7q74tet8u" xml:space="preserve">== PRESENTACIÓ PERSONAL ==
Hola! Em dic '''Gabi''' i tinc 21 anys i soc estudiant de '''DAW.'''

== FORMACIÓ ==
He estudiat cuina i pastisseria. Actualment estic estudiant Desenvolupament d'Aplicacions Web.

== AFICIONS ==
* Jugar a videojocs 
* Jugar a escacs 
* Escoltar música 
* Llegir manga


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  <page>
    <title>Plant Divisions (Phyla)/Charophyta</title>
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      <comment>Created page with &quot;[[Image:Chara overview.jpg|thumb|300px|right|This is a Charophyte.]] '''Charophyta''' ({{IPAc-en|k|ə|ˈ|r|ɒ|f|ᵻ|t|ə|,_|ˌ|k|ær|ə|ˈ|f|aɪ|t|ə}}) is a paraphyletic group of freshwater green algae, called '''charophytes''' ({{IPAc-en|ˈ|k|ær|ə|ˌ|f|aɪ|t|s}}), sometimes treated as a division,&lt;ref name=&quot;:1&quot;&gt;{{cite journal |last1=Lewis |first1=Louise A. |first2=Richard M. |last2=McCourt |year=2004 |title=Green algae and the origin of land plants |journal=[https://e...&quot;</comment>
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      <text bytes="5994" sha1="m4kvbksgrabhhyxghetqvgqqy02szpq" xml:space="preserve">[[Image:Chara overview.jpg|thumb|300px|right|This is a Charophyte.]]
'''Charophyta''' ({{IPAc-en|k|ə|ˈ|r|ɒ|f|ᵻ|t|ə|,_|ˌ|k|ær|ə|ˈ|f|aɪ|t|ə}}) is a paraphyletic group of freshwater green algae, called '''charophytes''' ({{IPAc-en|ˈ|k|ær|ə|ˌ|f|aɪ|t|s}}), sometimes treated as a division,&lt;ref name=&quot;:1&quot;&gt;{{cite journal |last1=Lewis |first1=Louise A. |first2=Richard M. |last2=McCourt |year=2004 |title=Green algae and the origin of land plants |journal=[https://en.wikipedia.org/wiki/American_Journal_of_Botany American Journal of Botany] |volume=91 |issue=10 |pages=1535–56 |doi=10.3732/ajb.91.10.1535 |pmid=21652308 |bibcode=2004AmJB...91.1535L }}&lt;/ref&gt; but also as a superdivision. The terrestrial plants, the Embryophytes emerged deep within Charophyta, possibly from terrestrial unicellular charophytes,&lt;ref&gt;{{cite journal|last1=de Vries|first1=J|last2=Archibald|first2=JM|title=Plant evolution: landmarks on the path to terrestrial life.|journal=The New Phytologist|date=March 2018|volume=217|issue=4|pages=1428–1434|doi=10.1111/nph.14975|pmid=29318635|doi-access=free|bibcode=2018NewPh.217.1428D}}&lt;/ref&gt; with the class Zygnematophyceae as a sister group.&lt;ref&gt;{{Cite journal|last=Del-Bem|first=Luiz-Eduardo|date=2018-05-31|title=Xyloglucan evolution and the terrestrialization of green plants|journal=New Phytologist|language=en|volume=219|issue=4|pages=1150–1153|doi=10.1111/nph.15191|pmid=29851097|issn=0028-646X|doi-access=free|bibcode=2018NewPh.219.1150D |hdl=1843/36860|hdl-access=free}}&lt;/ref&gt;&lt;ref name=&quot;:2&quot;&gt;{{Cite journal|last1=Ruhfel|first1=Brad R.|last2=Gitzendanner|first2=Matthew A.|last3=Soltis|first3=Pamela S.|last4=Soltis|first4=Douglas E.|last5=Burleigh|first5=J. Gordon|date=2014-02-17|title=From algae to angiosperms–inferring the phylogeny of green plants (Viridiplantae) from 360 plastid genomes|journal=BMC Evolutionary Biology|volume=14|issue=1 |page=23|doi=10.1186/1471-2148-14-23|issn=1471-2148|pmid=24533922|pmc=3933183 |doi-access=free |bibcode=2014BMCEE..14...23R }}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last1=Wickett|first1=Norman J.|last2=Mirarab|first2=Siavash|last3=Nguyen|first3=Nam|last4=Warnow|first4=Tandy|last5=Carpenter|first5=Eric|last6=Matasci|first6=Naim|last7=Ayyampalayam|first7=Saravanaraj|last8=Barker|first8=Michael S.|last9=Burleigh|first9=J. Gordon|date=2014-11-11|title=Phylotranscriptomic analysis of the origin and early diversification of land plants|journal=Proceedings of the National Academy of Sciences|language=en|volume=111|issue=45|pages=E4859–E4868|doi=10.1073/pnas.1323926111|issn=0027-8424|pmc=4234587|pmid=25355905|bibcode=2014PNAS..111E4859W|doi-access=free}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last1=Vries|first1=Jan de|last2=Stanton|first2=Amanda|last3=Archibald|first3=John M.|last4=Gould|first4=Sven B.|date=2016-02-16|title=Streptophyte Terrestrialization in Light of Plastid Evolution|journal=Trends in Plant Science|volume=21|language=en|issue=6|doi=10.1016/j.tplants.2016.01.021|pmid=26895731|issn=1360-1385|pages=467–476|bibcode=2016TPS....21..467D }}&lt;/ref&gt;&lt;ref&gt;Treatise on invertebrate paleontology. Part B. Protoctista 1. Volume1: Charophyta.[https://www.vinted.es/items/1376760800-treatise-on-invertebrate-paleontology-part-b-protoctista-1-volume1-charophyta?referrer=catalog]&lt;/ref&gt;

With the Embryophytes now cladistically placed in the Charophyta, it's a synonym of [[Streptophytes|Streptophyta]].&lt;ref name=&quot;:0&quot;&gt;{{Cite book|title=Handbook of the Protists|last1=Cook|first1=Martha E.|last2=Graham|first2=Linda E.|chapter=Chlorokybophyceae, Klebsormidiophyceae, Coleochaetophyceae |date=2017|publisher=Springer International Publishing|isbn=978-3-319-28147-6|editor-last=Archibald|editor-first=John M.|pages=185–204|language=en|doi=10.1007/978-3-319-28149-0_36|editor-last2=Simpson|editor-first2=Alastair G. B.|editor-last3=Slamovits|editor-first3=Claudio H.}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last1=Delwiche|first1=Charles F.|last2=Timme|first2=Ruth E.|title=Plants|journal=Current Biology|volume=21|issue=11|pages=R417–R422|doi=10.1016/j.cub.2011.04.021|pmid=21640897|year=2011|doi-access=free|bibcode=2011CBio...21.R417D }}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last1=Karol|first1=Kenneth G.|last2=McCourt|first2=Richard M.|last3=Cimino|first3=Matthew T.|last4=Delwiche|first4=Charles F.|date=2001-12-14|title=The Closest Living Relatives of Land Plants|journal=Science|language=en|volume=294|issue=5550|pages=2351–2353|doi=10.1126/science.1065156|issn=0036-8075|pmid=11743201|bibcode=2001Sci...294.2351K|s2cid=35983109}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last1=Lewis|first1=Louise A.|last2=McCourt|first2=Richard M.|date=2004|title=Green algae and the origin of land plants|url=https://onlinelibrary.wiley.com/doi/abs/10.3732/ajb.91.10.1535|journal=American Journal of Botany|language=en|volume=91|issue=10|pages=1535–1556|doi=10.3732/ajb.91.10.1535|pmid=21652308 |bibcode=2004AmJB...91.1535L |issn=1537-2197|url-access=subscription}}&lt;/ref&gt; The sister group of the charophytes are the Chlorophytes.
==Information==
Name Meaning: Chara-like plant

English Common Name: Charophytes

Approximate number of species described: 1,000
==Divisions==
Charophyceae – Chlorokybophyceae – Coleochaetophyceae – Klebsormidiophyceae – Mesostigmatophyceae – ''Streptofilum'' – Zygnematophyceae
===Cladistically included but traditionally excluded taxa===
Embryophytes
==Diagram==
[[File:2023 Charophyte.svg|thumb|500px|right|'''Representation of a charophyte''' {{ordered list| Mucilage|Cell wall(cellulose)|Vacuole|
Golgi apparatus, packages proteins|[[Mitochondria|Mitochondrion]], creates ATP (energy) for the cell (flat cristae)||Nucleus|Nucleolus|Endoplasmic reticulum, the transport network for molecules going to specific parts of the cell|Vesicles|Dense vesicle|Plastid membranes (two, primary)|Pyrenoid; center of carbon fixation|Isthmus|Polar lobe|Lateral lobe|First order|Second order|Third order}}]]
==References==
[[Wikipedia:Charophyta]]
[[Category:Plants]]
[[Category:Taxonomy]]
[[Category:Botany]]
[[Category:Biology]]</text>
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    <title>Animal Phyla/Chordata/Chordata Quiz</title>
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      <comment>This might be educational enough.</comment>
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&lt;quiz&gt;

{True or False, Chordates have an exoskeleton.
|type=&quot;()&quot;}
- True
+ False

{Which Chordates live on land?
|type=&quot;()&quot;}
- Actinopterygii
+ Tetrapods
- Sharks
- Thelodonts

{True or False, Chordates are radially symmetrical, just like their Echinoderm cousins.
|type=&quot;()&quot;}
- True
+ False

{True or False, Hemichordates are in the same phylum as Chordates.
|type=&quot;()&quot;}
- True
+ False

{True or false, Humans are in the same phylum as lungfish.
|type=&quot;()&quot;}
+ True
- False

&lt;/quiz&gt;
[[Category:Animals]]
[[Category:Quizzes]]
[[Category:Taxonomy]]
[[Category:Zoology]]
[[Category:Biology]]</text>
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        <username>Michael Ten</username>
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      <comment>Redirected page to [[Large language models]]</comment>
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      <text bytes="35" sha1="hrgyd44xmldx8jo08xgojfapyhx2csk" xml:space="preserve">#REDIRECT [[Large language models]]</text>
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      <contributor>
        <username>Michael Ten</username>
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      <comment>Redirected page to [[Large language models]]</comment>
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      <text bytes="35" sha1="hrgyd44xmldx8jo08xgojfapyhx2csk" xml:space="preserve">#REDIRECT [[Large language models]]</text>
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    <title>Large language models/Readings and learning media</title>
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      <comment>moving from main page. was very long there and a lot to sort through. limitless peace</comment>
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== Readings and learning media ==
=== Wikipedia ===
{{:Cross-domain_AI_topics}}
==== LLM Topics ====
Categories and lists:
: {{wc|Natural language processing}}
:: {{wc|Tasks of natural language processing}}
: {{wc|Large language models}}
:: {{wc|Generative pre-trained transformers}}
:: {{w|List of large language models}}

===== Basics (Wikipedia Readings) =====
: {{w|ChatGPT}}
: {{w|Large language model}}
: {{w|Prompt engineering}}
: {{w|GPT-4}}
: {{w|ChatGPT in education}}
: {{w|Turing test}}
: {{w|Natural-language understanding}}
: {{w|Word embedding}}
===== Intermediate (Wikipedia Readings) =====
: {{w|Transformer (deep learning architecture)}}
: {{w|Attention (machine learning)}}
: {{w|LLaMA}}
: {{w|Mistral AI}}
: {{w|Foundation model}}
: {{w|LangChain}}
: {{w|Generative pre-trained transformer}} (GPT)
: {{w|GitHub Copilot}}

===== Advanced (Wikipedia Readings) =====
: {{w|Reflection (artificial intelligence)}}
: {{w|Reasoning language model}}
: {{w|Retrieval-augmented generation}}
: {{w|Knowledge distillation}}
: {{w|Model compression}}
: {{w|History of natural language processing}}
: {{w|Neural scaling law}}
: {{w|GitHub Copilot}}
: {{w|Automated reasoning}}
: {{w|Mixture of experts}}
: {{w|Gemini (language model)}}
: {{w|Auto-GPT}}
: {{w|VideoPoet}}
: {{w|Artificial intelligence in Wikimedia projects}}
: {{w|Artificial intelligence content detection}}
: {{w|Language model}}
:: {{w|Language model benchmark}}
:: {{w|Language_model#Evaluation_and_benchmarks|Evaluation and benchmarks}}
::: {{w|MMLU}}
: {{wc|Tasks of natural language processing}}
:: {{w|Question answering}}
:: {{w|Sentiment analysis}}
:: {{w|Named-entity recognition}}
: {{w|Zero-shot learning}}
: More
:: Internals
::: {{w|Word2vec}}
::: {{w|Seq2seq}}
::: {{w|GloVe}}
:: {{w|List of large language models}}
::: {{w|BERT (language model)|BERT}}
::: {{w|T5 (language model)|T5}}
::: {{w|Llama (language model)|Llama}}
::: {{w|Chinchilla (language model)|Chinchilla AI}}
::: {{w|PaLM}}
::: {{w|Generative pre-trained transformer|GPT}}
::: {{w|GPT-1|1}}, {{w|GPT-2|2}}, {{w|GPT-3|3}}, {{w|GPT-J|J}}
:::: {{w|ChatGPT}}
:::: {{w|GPT-4|4}}, {{w|GPT-4o|4o}}
:::: {{w|OpenAI o1|o1}}, {{w|OpenAI o3|o3}}
::: {{w|Claude (language model)|Claude}}
::: {{w|Gemini (language model)|Gemini}}
:::: {{w|Gemini (chatbot)|chatbot}}
::: {{w|Grok (chatbot)|Grok}}
:: {{w|LaMDA}}
::: {{w|BLOOM (language model)|BLOOM}}
::: {{w|Project Debater}}
::: {{w|IBM Watson}}
::: {{w|IBM Watsonx}}
::: {{w|IBM Granite|Granite}}
::: {{w|Huawei PanGu|PanGu-Σ}}
::: {{w|DeepSeek}}
::: {{w|Qwen}}

===External===
: [https://arena-chapter1-transformer-interp.streamlit.app/ Transformer Interpretability, ARENA]
: [https://rdi.berkeley.edu/llm-agents/f24 LLM agents course, Berkeley], [https://www.youtube.com/watch?v=QL-FS_Zcmyo @youtube]
: https://anthropic.skilljar.com/
: https://hf.co/learn/, [https://hf.co/learn/smol-course Smol LLM fine-tuning course]
: https://academy.openai.com/
: https://cookbook.openai.com/
: https://academy.langchain.com/
: [https://medium.com/@tom_21755/understanding-causal-llms-masked-llm-s-and-seq2seq-a-guide-to-language-model-training-d4457bbd07fa Understanding Causal LLM’s, Masked LLM’s, and Seq2Seq: A Guide to Language Model Training Approaches]
: Docs
:: https://docs.x.ai/
:: https://platform.deepseek.com/
:: https://platform.openai.com/
:: https://docs.anthropic.com/
:: https://docs.mistral.ai/
: Papers, publications
:: https://huggingface.co/papers
:: [https://arxiv.org/abs/2201.11903 Chain-of-Thought Prompting Elicits Reasoning in Large Language Models, 2022]
:: [https://arxiv.org/abs/2106.09685 LoRA: Low-Rank Adaptation of Large Language Models, 2021]
:: [https://arxiv.org/abs/1706.03762 Attention Is All You Need, 2017]
: Articles
:: https://www.pinecone.io/learn/retrieval-augmented-generation/
:: [https://stpp.fordschool.umich.edu/tags/large-language-models Large Language Models] - Articles
:: [https://hai.stanford.edu/news/how-large-language-models-will-transform-science-society-and-ai How Large Language Models Will Transform Science, Society, and AI]
:: [https://insights.sei.cmu.edu/blog/harnessing-the-power-of-large-language-models-for-economic-and-social-good-foundations/ Harnessing the Power of Large Language Models For Economic and Social Good: Foundations]
:: [https://courses.grainger.illinois.edu/CS447/sp2023/Slides/Lecture27.pdf Lecture 27: Intro to Large Language Models]

==== Deep Reinforcement Learning ====
: [https://hf.co/learn/deep-rl-course/unit0/introduction Deep RL]
:: Huggy, Q-Learning

==== Model Context Protocol (MCP) Course ====
: [https://huggingface.co/learn/mcp-course/unit0/introduction MCP Course]
:: Continue, Gradio, Hugging Face Hub, Claude Code, GitHub, Slack

==== AI Agents Course ====
[https://hf.co/learn/agents-course/unit0/introduction Hugging Face AI Agents Course]
: [https://hf.co/learn/agents-course/unit1/introduction Introduction to Agents]
:: [https://huggingface.co/learn/agents-course/unit1/agent-steps-and-structure Thought-Action-Observation Cycle]
: [https://hf.co/learn/agents-course/unit2/introduction Frameworks for AI Agents]
:: [https://hf.co/learn/agents-course/unit2/smolagents/introduction smolagents] 
::: [https://huggingface.co/learn/agents-course/unit2/smolagents/code_agents code agents]
::: [https://huggingface.co/learn/agents-course/unit2/smolagents/tools tools]
::: [https://huggingface.co/learn/agents-course/unit2/smolagents/multi_agent_systems multi-agent]
::: ... [https://huggingface.co/docs/smolagents/index docs]
:: [https://hf.co/learn/agents-course/unit2/llama-index/introduction LlamaIndex]
::: ... [https://docs.llamaindex.ai/en/stable/understanding/ docs]
:: [https://hf.co/learn/agents-course/unit2/langgraph/introduction LangGraph]
::: ... [https://academy.langchain.com/courses/intro-to-langgraph Introduction to LangGraph], [https://langchain-ai.github.io/langgraph/ docs]
: [https://hf.co/learn/agents-course/unit3/agentic-rag/introduction Use Case for Agentic RAG]
:: [https://huggingface.co/learn/agents-course/unit3/agentic-rag/invitees tools]
: bonus
:: [https://hf.co/learn/agents-course/bonus-unit1/introduction Fine-tuning an LLM for Function-calling]
:: [https://hf.co/learn/agents-course/bonus-unit2/introduction Agent Observability and Evaluation]

==== LLM Course ====
Introductory course about natural large language models (LLMs) and language processing (NLP) using libraries from the Hugging Face ecosystem &amp;ndash; Transformers, Datasets, Tokenizers, and Accelerate.

: [https://hf.co/course/chapter0/1 '''LLM Course''']
:: [https://hf.co/course/chapter1/1 Transformer models]
::: [https://hf.co/course/chapter1/2 NLP and LLM], [https://hf.co/course/chapter1/3 What], [https://hf.co/course/chapter1/4 How], [https://hf.co/course/chapter1/5 Encoder], [https://hf.co/course/chapter1/6 Decoder], [https://hf.co/course/chapter1/7 Sequence-to-sequence], [https://hf.co/course/chapter1/8 Bias and limitations], 
:: [https://hf.co/course/chapter2/1 Using transformers]:
::: [https://hf.co/course/chapter2/2 pipeline], [https://hf.co/course/chapter2/3 models], [https://hf.co/course/chapter2/4 tokenizer], [https://hf.co/course/chapter2/5 batching], decoding, padding, attention mask
:: [https://hf.co/course/chapter3/1 Fine-tuning a pretrained model]:
::: [https://hf.co/course/chapter3/2 Preprocessing]&lt;small&gt;: tokenization, padding&lt;/small&gt;, [https://hf.co/course/chapter3/3 Fine-tuning], [https://hf.co/course/chapter3/4 Full training], map, [https://hf.co/docs/datasets/index dataset], dynamic padding, batch, collate function, train, predict, evaluate, [https://github.com/huggingface/accelerate accelerate]
:: [https://hf.co/course/chapter4/1 Sharing models and tokenizers]:
::: [https://hf.co/course/chapter4/2 Using], [https://hf.co/course/chapter4/3 Sharing]: push_to_hub, upload_file, Repository, git lfs, [https://hf.co/course/chapter4/4 Model card]
:: [https://hf.co/course/chapter5/1 The datasets library]:
::: [https://hf.co/course/chapter5/2 Loading dataset], [https://hf.co/course/chapter5/3 Slicing], batch, DataFrame, validation, splitting, [https://hf.co/course/chapter5/4 Big]: streaming, [https://hf.co/course/chapter5/5 Creating], [https://hf.co/course/chapter5/6 Semantic search]: embedding, [https://faiss.ai/ FAISS]
:: [https://hf.co/course/chapter6/1 The tokenizers library]:
::: [https://hf.co/course/chapter6/2 Training tokenizer], [https://hf.co/course/chapter6/3 Fast], grouping, [https://hf.co/course/chapter6/3b QnA], [https://hf.co/course/chapter6/4 Pre-tokenization], ([https://hf.co/docs/tokenizers/api/models models],[https://hf.co/docs/tokenizers/api/trainers trainers]), [https://hf.co/course/en/chapter6/5 Byte-Pair Encoding (BPE)], [https://hf.co/course/chapter6/6 WordPiece], [https://hf.co/course/chapter6/7 Unigram], [https://hf.co/course/chapter6/8 Building]: [https://hf.co/docs/tokenizers/api/post-processors post processors], [https://hf.co/docs/tokenizers/components#decoders decoders]
:: [https://hf.co/course/chapter7/1 Main nlp tasks]:
::: [https://hf.co/course/chapter7/2 Token classification], metrics, perplexity, [https://hf.co/course/chapter7/3 Fine-tuning a masked LM], [https://hf.co/course/chapter7/4 Translation], [https://hf.co/course/chapter7/5 Summarization], [https://hf.co/course/chapter7/6 CLM], [https://hf.co/course/chapter7/7 QnA]
:: [https://hf.co/course/chapter8/1 How to ask for help]
::: [https://hf.co/course/chapter8/2 Error], [https://hf.co/course/chapter8/3 Forums], [https://hf.co/course/chapter8/4 Debugging], [https://hf.co/course/chapter8/5 Issue]
:: [https://hf.co/course/chapter9/1 Gradio Demos]
::: [https://hf.co/course/chapter9/2 Building], [https://hf.co/course/chapter9/3 Interface class], [https://hf.co/course/chapter9/4 Sharing], [https://hf.co/course/chapter9/5 Integration], [https://hf.co/course/chapter9/7 Gradio Blocks]
:: [https://hf.co/course/chapter10/1 Curate high-quality datasets]
:: [https://hf.co/course/chapter11/1 Fine-tune Large Language Models]
:: [https://hf.co/course/chapter12/1 Build Reasoning Models]
:: [https://hf.co/course/events/1 Course Events]

==== Hugging Face docs ====
: https://hf.co/docs
: [https://hf.co/spaces/HuggingFaceTB/smol-training-playbook The Smol Training Playbook: The Secrets to Building World-Class LLMs]
===== Core libraries =====
::: [https://hf.co/docs/transformers Transformers] &amp;ndash; State-of-the-art ML for Pytorch, TensorFlow, and JAX.
:::: [https://hf.co/docs/transformers/pipeline_tutorial Inference, Tutorials]
::::: {{colbegin|2}} Run inference with pipelines, Write portable code with AutoClass, Preprocess data, Fine-tune a pretrained model, Train with a script, Set up distributed training with Accelerate, Load and train adapters with PEFT, Share your model, Agents 101, Agents, supercharged - Multi-agents, External tools, and more, Generation with LLMs, Chatting with Transformers {{colend}}
::::: [https://hf.co/docs/transformers/pipeline_tutorial Pipline]
::::: [https://hf.co/docs/transformers/llm_tutorial LLM]
::::: [https://hf.co/docs/transformers/conversations Chat]
:::: Tasks
::::: [https://hf.co/docs/transformers/tasks/sequence_classification NLP]
:::::: Text classification, Token classification, Question answering, Causal language modeling, Masked language modeling, Translation, Summarization, Multiple choice
::::: [https://hf.co/docs/transformers/tasks/audio_classification Audio], [https://hf.co/docs/transformers/tasks/image_classification Vision],[https://hf.co/docs/transformers/tasks/image_captioning Multimodal], [https://hf.co/docs/transformers/generation_strategies Generation], [https://hf.co/docs/transformers/tasks/idefics Prompting]
:::: [https://hf.co/docs/transformers/fast_tokenizers Developer guides]
:::: [https://hf.co/docs/transformers/quantization/overview Quantization]
:::: [https://hf.co/docs/transformers/performance Performance]
:::: [https://hf.co/docs/transformers/contributing Contributing]
:::: [https://hf.co/docs/transformers/philosophy Conceptual guides]
:::: [https://hf.co/docs/transformers/main_classes/agent API]
::::: [https://hf.co/docs/transformers/main_classes/pipelines#transformers.pipeline pipeline] &amp;ndash; simple interface for inference with models.
::::: ...
:::: [https://hf.co/docs/transformers/model_doc/albert Text models]
:::: [https://hf.co/docs/transformers/internal/modeling_utils Internal helpers]
:::: [https://hf.co/docs/transformers/model_doc/auto#auto-classes Auto classes]: AutoConfig, AutoModel, and AutoTokenizer. The from_pretrained method.
:::: [https://hf.co/docs/transformers/main_classes/trainer#transformers.Trainer Trainer] and [https://hf.co/docs/transformers/main_classes/trainer#transformers.TrainingArguments TrainingArguments] 
:::: [https://hf.co/docs/transformers/main/en/glossary Glossary]
::::: [https://huggingface.co/docs/transformers/main/en/glossary#head model head]
::: [https://hf.co/docs/datasets Datasets] &amp;ndash; Access and share datasets for computer vision, audio, and NLP tasks.
:::: [https://hf.co/docs/datasets/tutorial Tutorials]
:::: [https://hf.co/docs/datasets/how_to How-to guides]
:::: [https://hf.co/docs/datasets/about_arrow Conceptual guides]
:::: [https://hf.co/docs/datasets/package_reference/main_classes Reference]
::: [https://hf.co/docs/accelerate Accelerate] &amp;ndash; Easily train and use PyTorch models with multi-GPU, TPU, mixed-precision.
::: [https://hf.co/docs/tokenizers Tokenizers] &amp;ndash; Fast tokenizers, optimized for both research and production.
:::: Main components: Normalizers, Pre-tokenizers, Models, Post-Processors, Decoders
:::: More APIs: ... Input Sequences, Encode Inputs, Tokenizer, Encoding, Added Tokens, Visualizer

===== More docs =====
:: [https://hf.co/docs/hub Hub] &amp;ndash; Host Git-based models, datasets and Spaces on the Hugging Face Hub.
:: [https://hf.co/docs/diffusers Diffusers] &amp;ndash; State-of-the-art diffusion models for image and audio generation in PyTorch.
:: [https://hf.co/docs/huggingface_hub Hub Python Library] &amp;ndash; Client library for the HF Hub: manage repositories from your Python runtime.
:: [https://hf.co/docs/huggingface.js Huggingface.js] &amp;ndash; A collection of JS libraries to interact with Hugging Face, with TS types included.
:: [https://hf.co/docs/transformers.js Transformers.js] &amp;ndash; Community library to run pretrained models from Transformers in your browser.
:: [https://hf.co/docs/api-inference Inference API (serverless)] &amp;ndash; Experiment with over 200k models easily using the serverless tier of Inference Endpoints.
:: [https://hf.co/docs/inference-endpoints Inference Endpoints (dedicated)] &amp;ndash; Easily deploy models to production on dedicated, fully managed infrastructure.
:: [https://hf.co/docs/peft PEFT] &amp;ndash; Parameter efficient fine-tuning methods for large models
::: [https://hf.co/docs/peft/tutorial/peft_model_config Tutorial]
::: [https://hf.co/docs/peft/task_guides/prompt_based_methods PEFT method guides]
:::: LoRA, IA3
::: [https://hf.co/docs/peft/developer_guides/model_merging Developer guides]
:::: Model merging, Quantization, LoRA, Custom models, Adapter injection, Mixed adapter types, torch.compile, Contribute to PEFT, Troubleshooting, PEFT checkpoint format
::: [https://hf.co/docs/peft/accelerate/deepspeed Acceselerate]
:::: DeepSpeed, Fully Sharded Data Parallel
::: [https://hf.co/docs/peft/conceptual_guides/adapter Conceptual guides]
:::: Adapters, Soft prompts: Prompt tuning, Prefix tuning, P-tuning, Multitask prompt tuning, CPT; IA3, OFT/BOFT
::: [https://hf.co/docs/peft/package_reference/auto_class API reference]
:::: [https://hf.co/docs/peft/package_reference/auto_class Main classes]
::::: AutoPeftModel, PEFT model, PEFT types, Configuration, Tuner
:::: [https://hf.co/docs/peft/package_reference/adalora Adapters]
::::: {{colbegin|2}} AdaLoRA, IA3, Llama-Adapter, LoHa, LoKr, LoRA, X-LoRA, LyCORIS, Multitask Prompt Tuning, OFT, BOFT, Polytropon, P-tuning, Prefix tuning, Prompt tuning, Layernorm tuning,   VeRA, FourierFT, VB-LoRA, HRA, CPT, Bone{{colend}}
::: [https://hf.co/docs/peft/package_reference/merge_utils Utilities]
:::: Model merge, Helpers, Hotswapping adapters
:: [https://hf.co/docs/optimum Optimum] &amp;ndash; Fast training and inference of HF Transformers with easy to use hardware optimization tools.
:: [https://hf.co/docs/optimum-neuron AWS Trainium &amp;amp; Inferentia] &amp;ndash; Train and Deploy Transformers &amp;amp; Diffusers with AWS Trainium and AWS Inferentia via Optimum
:: [https://hf.co/docs/evaluate Evaluate] &amp;ndash; Evaluate and report model performance easier and more standardized.
::: types: metrics, comparisons, measurements
:: [https://hf.co/tasks Tasks]
::: extraction, question answering, classification, generation ...
:: [https://hf.co/docs/dataset-viewer Dataset viewer] &amp;ndash; API to access the contents, metadata and basic statistics of all Hugging Face Hub datasets.
::: Splits and subsets, [https://github.com/huggingface/dataset-viewer dataset-viewer]
:: [https://hf.co/docs/trl TRL] &amp;ndash; Transformer Reinforcement Learning
:::  reward modeling, fine-tuning, optimizations, 
:: [https://hf.co/docs/sagemaker Amazon SageMaker] &amp;ndash; Train and Deploy Transformer models with Amazon SageMaker and Hugging Face Deep Learning Containers (DLC).
:: [https://hf.co/docs/timm timm] &amp;ndash; Pytorch Image Models.
::: State-of-the-art computer vision models, layers, optimizers, training/evaluation, and utilities.
:: [https://hf.co/docs/safetensors Safetensors] &amp;ndash; Simple, safe way to store and distribute neural networks weights.
:: [https://hf.co/docs/text-generation-inference Text Generation Inference (TGI)] &amp;ndash; Toolkit to serve Large Language Models.
::: Conceptual Guides
::::  [https://hf.co/docs/text-generation-inference/conceptual/chunking V3 update, caching and chunking]
::::  [https://hf.co/docs/text-generation-inference/conceptual/streaming Streaming]
::::  [https://hf.co/docs/text-generation-inference/conceptual/quantization Quantization]
::::  [https://hf.co/docs/text-generation-inference/conceptual/tensor_parallelism Tensor Parallelism]
::::  [https://hf.co/docs/text-generation-inference/conceptual/paged_attention PagedAttention]
::::  [https://hf.co/docs/text-generation-inference/conceptual/safetensors Safetensors]
::::  [https://hf.co/docs/text-generation-inference/conceptual/flash_attention Flash Attention]
::::  [https://hf.co/docs/text-generation-inference/conceptual/speculation Speculation (Medusa, ngram)]
::::  [https://hf.co/docs/text-generation-inference/conceptual/guidance How Guidance Works (via outlines)]
::::  [https://hf.co/docs/text-generation-inference/conceptual/lora LoRA (Low-Rank Adaptation)]
::::  [https://hf.co/docs/text-generation-inference/conceptual/external External Resources]

:: [https://hf.co/docs/text-embeddings-inference Text Embeddings Inference] &amp;ndash; Toolkit to serve Text Embedding Models.
:: [https://hf.co/docs/competitions Competitions] &amp;ndash; Create your own competitions on Hugging Face.
:: [https://hf.co/docs/bitsandbytes Bitsandbytes] &amp;ndash; Toolkit to optimize and quantize models.
:: [https://hf.co/docs/optimum-tpu Google TPUs] &amp;ndash; Deploy models on [https://cloud.google.com/tpu/docs Google TPUs] via Optimum.
:: [https://hf.co/docs/chat-ui Chat UI] &amp;ndash; Open source chat frontend, powers the [https://hf.co/chat HuggingChat] app.
:: Extras
::: [https://hf.co/docs/hugs Hugging Face Generative AI Services (HUGS)] 
::: [https://hf.co/docs/leaderboards Leaderboards] &amp;ndash; Create your own Leaderboards on Hugging Face.
::: [https://hf.co/docs/autotrain AutoTrain] &amp;ndash; AutoTrain API and UI.
:::: [https://hf.co/autotrain autotrain]
::: [https://huggingface.co/docs/smolagents/index smolagents]

===Videos===
* [https://www.youtube.com/watch?v=5sLYAQS9sWQ How Large Language Models Work]
* [https://www.youtube.com/watch?v=JhCl-GeT4jw Large Language Models and The End of Programming - CS50 Tech Talk with Dr. Matt Welsh]
* [https://www.youtube.com/watch?v=yBI1nPep72Q LMStudio Tutorial Run ANY Open-Source Model LOCALLY]
* [https://www.youtube.com/watch?v=UU1WVnMk4E8 Create a Large Language Model from Scratch with Python – Tutorial]
* [https://www.youtube.com/watch?v=eC6Hd1hFvos Fine-tuning Large Language Models (LLMs) | w/ Example Code]

===Data sets===
* [https://hf.co/blog/Pclanglais/two-trillion-tokens-open Releasing the largest multilingual open pretraining dataset]
:: [https://hf.co/datasets/PleIAs/common_corpus Common Corpus]
:: [https://hf.co/datasets/PleIAs/common_corpus/tree/main Files and versions]</text>
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|Date=2026-09-18
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
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      <comment>{{Information
|Description=Work2.1A: Libraries (20260918 - 20260917)
|Source={{own|Young1lim}}
|Date=2026-09-18
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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      <text bytes="264" sha1="cezucvxipsel0og53q8vjh8dj9owrch" xml:space="preserve">== Summary ==
{{Information
|Description=Work2.1A: Libraries (20260918 - 20260917)
|Source={{own|Young1lim}}
|Date=2026-09-18
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
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  <page>
    <title>Artificial intelligence/Checking AI output with a second agent</title>
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        <username>Evgenii Arsentev</username>
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      <comment>New learning resource: checking an AI agent's output with a second agent, and how to measure whether the check helps</comment>
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      <text bytes="6783" sha1="1mwgw2f3rq22kunl7ryl1en1t02vcsf" xml:space="preserve">{{Short description|How to check the work of an AI agent with a second agent, and how to tell whether the check is doing anything}}

This learning resource is a sub-page of [[Artificial intelligence]]. It is about a practical question for anyone who now delegates work to AI agents: '''how do you find out whether the result is right, when the system reports a wrong answer in exactly the same confident voice as a right one?'''

It teaches one pattern, the second agent as a checker, and it treats that pattern as something to measure rather than to trust.

{{RightTOC}}

== Learning objectives ==

After working through this resource a learner should be able to:

* explain why a single agent run gives no usable signal about its own correctness;
* set up a check in which a second agent, with a fresh context, looks for defects in the first agent's output;
* choose between three arrangements of that check and say what each one costs;
* design a small experiment that shows whether the check catches anything, instead of assuming it does;
* describe what a check cannot catch, and where a person still has to decide.

== 1. Why one answer is not enough ==

A language model produces fluent text whether or not the underlying claim is true. It can invent a reference, skip a case the task never mentioned, or report a defect as repaired when the repair did not happen. The tone stays level in all three situations, so the reader gets no cue from the output itself.

This matters more for agents than for chat. An agent runs many steps without a person watching, and its later steps build on its earlier ones. A wrong intermediate result is not discarded, it is used.

The size of that hidden layer can be measured. In a published measurement of 722 agent sessions and 150,902 model calls, 52% of the calls came from subagents rather than from the top-level agent, each with its own context and its own permissions (Arsentev, 2026, DOI 10.5281/zenodo.22759216). Most of what an agent system does is therefore invisible in the final answer a person reads.

== 2. The pattern: a second agent that starts fresh ==

The check is a separate run with a different instruction. The first agent solves the task. The second agent receives the output, a copy of the task, and one job: find what is wrong with this.

Two properties make it work:

* '''No authorship.''' The second agent did not produce the answer, so it has nothing to defend. A model asked to re-check its own answer tends to confirm it.
* '''A fresh context.''' The first agent's reasoning does not travel with the output, so the second agent reconstructs the problem instead of inheriting the path that produced the mistake.

Neither property is magic. Both are cheap.

== 3. Three arrangements ==

{| class=&quot;wikitable&quot;
! Arrangement !! What the second agent does !! Typical cost
|-
| Verify || Re-derives the result independently and compares || Two full runs
|-
| Attack || Tries to produce an input on which the result fails || One run plus a short adversarial loop
|-
| Review || Reads the artefact against a checklist and reports defects by location || Much less than a full run
|}

'''Exercise 1.''' You have a task whose output is a 300-line script and whose failure mode is a wrong edge case. Which arrangement fits, and why is ''Verify'' a poor choice here? ''(A hint: the cost of re-deriving a script is close to the cost of writing it.)''

== 4. Writing the checker's instruction ==

The instruction decides what comes back. Three rules follow from practice:

# Ask for defects with coordinates. &quot;Line 42 reuses the closed connection&quot; is actionable. &quot;The code could be more robust&quot; is not.
# Forbid a verdict without evidence. The checker must quote the part of the artefact it is judging.
# Give the acceptance criteria of the original task. A checker that does not know what &quot;done&quot; means invents its own standard, and then the disagreement is about the standard rather than about the work.

A vague task produces the same failure on both sides. An agent given an unclear instruction does not stop to ask; it completes the task confidently and incorrectly, and the mistake is not visible at first reading.

== 5. Does the check actually catch anything? ==

This is the part most teams skip. The pattern is easy to adopt and easy to believe in, so it is worth measuring rather than assuming.

A minimal experiment:

# Collect a set of tasks whose correct outcome you can decide independently, for example by running tests.
# Run each task once without a checker and once with a checker, keeping everything else fixed.
# Record three numbers per task: whether the final artefact passed, how many defects the checker reported, and how many of those reports were false.
# Compare pass rates, and look at the false reports separately. A checker that reports many phantom defects costs attention, which is the scarce resource.

Report the spread across repeats, not a single run. Agent runs are not deterministic: the same task can take a different number of model calls on each attempt, so a difference between two single runs says very little.

'''Exercise 2.''' You measure 12 tasks, 6 repeats each, and the checker raises the pass rate from 7/12 to 9/12 on average. What would you need to claim that the improvement is real rather than noise? ''(Consider a permutation test over the repeats, and consider how much of the difference comes from one task.)''

== 6. What a second agent cannot do ==

* It cannot supply a fact that is absent from the material. If the task needs a number nobody has, both agents will agree on a plausible one.
* It cannot resolve a disagreement about goals. Whether a product should do X at all is not a defect report.
* It cannot carry responsibility. Someone has to own the outcome, and that someone is a person.

== 7. Suggested activities ==

* Take a task you recently delegated to an agent. Write the checker instruction for it in five lines, using the three rules in section 4.
* Run the minimal experiment from section 5 on ten small tasks. Publish the counters, including the false reports.
* Read the released run-level data of an agent workload and check how much of the cost sits in re-read context rather than in generation (Arsentev, 2026, DOI 10.5281/zenodo.22699668).

== References ==

* Arsentev, E. (2026). ''The Context Economy of Agentic LLM Sessions: Where the Money Actually Goes.'' Technical report. DOI: 10.5281/zenodo.22759216
* Arsentev, E. (2026). ''Clear Every Third Task: A Measured U-Curve in the Context Economy of Coding Agents.'' Dataset and harness. DOI: 10.5281/zenodo.22699668

== See also ==

* [[Artificial intelligence/AI content engine economics]]
* [[Large language models/Context economy of agent runs]]

[[Category:Artificial intelligence]]</text>
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  <page>
    <title>User talk:UU3231448</title>
    <ns>3</ns>
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      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Welcome</comment>
      <origin>2833735</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2330" sha1="b3ufv6c2ep5aqtpvarrstuib9cjvowt" xml:space="preserve">==Welcome==
{{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]],  UU3231448!'''|width=100%}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Jtneill|me personally]] if you would like some [[Help:Contents|help]].

Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. Using the signature icon [[File:OOjs UI icon signature-ltr.svg]] makes it simple.

We invite you to [[Wikiversity:Be bold|be bold]] and [[Wikiversity|assume good faith]]. Please abide by our [[Wikiversity:Civility|civility]], [[Wikiversity:Privacy policy|privacy]], and [[Foundation:Terms of Use|terms of use]] policies.

To find your way around, check out:
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* [[Wikiversity:Introduction|Introduction to Wikiversity]]
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* [[Wikiversity:Introduction explore|Explore]] links in left-hand navigation menu
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* Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]]
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&lt;/div&gt;
&lt;br clear=&quot;both&quot;/&gt;

To get started, experiment in the [[wikiversity:sandbox|sandbox]] or on [[special:mypage|your userpage]].

See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:04, 18 September 2026 (UTC)&lt;/div&gt;
&lt;!-- Template:Welcome --&gt;
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      <comment>Topic development feedback</comment>
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      <text bytes="6303" sha1="8zefwk9shducpt66e4kyj9cn4f0gmgk" xml:space="preserve">== Heading casing ==
{| style=&quot;float: center; background:transparent;color:inherit;&quot;
|-
| [[File:Crystal Clear app ktip.svg|48px|left]]
| {{#if:UU3231448|Hi [[User:UU3231448|UU3231448]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:&lt;br&gt;
&lt;big&gt;&lt;big&gt;Self-determination theory&lt;/big&gt;&lt;/big&gt;
rather than
&lt;big&gt;&lt;big&gt;Self-Determination Theory&lt;/big&gt;&lt;/big&gt;

Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]]

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:28, 18 September 2026 (UTC)
|}

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed)
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 1-level --&gt;
# Basic, [[Motivation and emotion/Assessment/Major project/Structure|1-level heading structure]] – could benefit from further development, perhaps using a 2-level structure (i.e., use subheadings)
&lt;!-- Alignment with focus questions --&gt;
# Insufficient alignment between sub-title, focus questions, and top-level headings
&lt;!-- GenAI ---&gt;
# Are the headings based on [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|3=
&lt;!-- Overview--&gt;
# Reasonably good
&lt;!-- GenAI ---&gt;
# Does this section include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, it needs to be acknowledged as such in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Scenario --&gt;
# Basic, relevant scenario; would benefit from further development to make it more compelling and illustrative
# Add an image to the scenario to help attract reader interest
&lt;!-- Description --&gt;
# A promising description of the problem/topic is planned or presented
# Focus more on the psychological theory (and evidence) that the author
&lt;!-- Focus questions --&gt;
&lt;!-- Alignment and quality --&gt;
# Develop closer alignment between the sub-title, focus questions, and top-level headings
# Use bullet-points (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Promising development
# Insufficient use of citations
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is excellent (i.e., not too little/narrow or too big/broad)
&lt;!-- Theory and research --&gt;
# Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples.
&lt;!-- Other --&gt;
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- GenAI ---&gt;
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion hasn't been developed
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --
# Relevant figure(s) presented
&lt;!-- Caption --&gt;
# Figure caption(s) should explain how the image connects to key points being made in the main text
&lt;!-- Cite --&gt;
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
&lt;!-- Size --&gt;
# Consider increasing image size(s) (especially if they have text) to make them easier to view
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Consider including quiz question(s) about the take-home messages
&lt;!-- Tables --&gt;
# Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Insufficient
# Only cite sources that you have consulted
&lt;!-- Systematic reviews --&gt;
# What are the top peer-reviewed theory and research journal articles about this topic?
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## capitalisation
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## One of two link types provided
### Also link to related [[Motivation and emotion/Book|motivation and emotion book chapters]]
&lt;!-- External links --&gt;
# External links
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant external resources about this topic
|9=
&lt;!-- User page --&gt;
# Basic
&lt;!-- Description about self --&gt;
# Very brief description about self – consider expanding
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]].
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:28, 18 September 2026 (UTC)</text>
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|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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== Licensing ==
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